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Year 3 Parallel and Perpendicular Lines

parallel and perpendicular lines problem solving year 3

Lines of Symmetry and Parallel or Perpendicular Lines

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Parallel, Perpendicular and Intersecting Lines Worksheets

This module deals with parallel, perpendicular and intersecting lines. A variety of pdf exercises and word problems will help improve the skills of students in grade 3 through grade 8 to identify and differentiate between parallel, perpendicular and intersecting lines. Some of them are absolutely free of cost!

Printable Charts

Printable Charts

Self-descriptive charts will help you learn symbolic representation and characteristics of parallel, perpendicular and intersecting lines.

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Identify the Type

Identify the Type

These printable worksheets will assist the students to differentiate the lines based on their geometrical properties. Identify whether the lines are parallel, perpendicular or intersecting lines.

Types of Lines: MCQ

Types of Lines: MCQ

From the given figure, identify each pair of lines as parallel, perpendicular or intersecting lines. Choose the correct answer from the given options.

Pair of Lines in Geometrical Figures

Pair of Lines in Geometrical Figures

Whether it is identifying the types of lines in each geometrical figure, or finding out the number of parallel and perpendicular lines, these printable worksheets for grade 4, grade 5, and grade 6 have both the exercises covered for you.

Parallel Lines and the Transversal

Parallel Lines and the Transversal

From the given sketch, analyze the transversal line. Identify the given lines and answer the questions in the given pdf worksheets.

Real-Life Objects: Parallel vs Perpendicular

Real-Life Objects: Parallel vs Perpendicular

In this set of printable worksheets for 3rd grade, 4th grade, and 5th grade kids are required to identify whether the pair of lines is parallel or perpendicular from the objects they are using in day-to-day life.

Parallel and Perpendicular Streets - Road Map

Parallel and Perpendicular Streets - Road Map

Examine the given road map to identify parallel and perpendicular streets. Answer the questions related to the road map.

Prove the Relationship: Points and Slopes

Prove the Relationship: Points and Slopes

This section consists of exercises related to slope of the line. Apply slope formula, find whether the lines are parallel or perpendicular. Justify your answer.

Points and Slopes: Finding Unknown

Points and Slopes: Finding Unknown

In these pdf worksheets, the relation between the lines is given. Find the missing coordinate in each problem.

Prove the Relationship: Equations and Slopes

Prove the Relationship: Equations and Slopes

Apply the slope formula for the given equations. Find whether the lines are parallel or perpendicular. Justify your answer.

Equations and Slopes: Finding Unknown

Equations and Slopes: Finding Unknown

In these printable worksheets for 6th grade, 7th grade, and 8th grade students, the relation between the lines is given. Find the unknown parameter

Equations, Points and Slopes

Equations, Points and Slopes

Calculate the slope of the equation. Prove that the lines are parallel or perpendicular. Justify your answer.

Related Worksheets

» Lines, Rays and Line Segments

» Points, Lines and Planes

» Angles Formed by a Transversal

» Angles

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If children need more practice on parallel and perpendicular lines, this worksheet is a great way to consolidate and extend their learning. The questions are presented in a simple diagram format with space for them to write their answers on the sheet.

Children can check their work using the accompanying answers.

  • Key Stage: Key Stage 2
  • Subject: Maths
  • Topic: Properties of Shapes
  • Topic Group: Geometry
  • Year(s): Year 3
  • Media Type: PDF
  • Resource Type: Worksheet
  • Last Updated: 24/10/2023
  • Resource Code: M2WAC1471
  • Curriculum Point(s): Identify horizontal and vertical lines and pairs of perpendicular and parallel lines.

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Parallel and Perpendicular Lines

How to use Algebra to find parallel and perpendicular lines

Parallel Lines

How do we know when two lines are parallel ?

Their slopes are the same!

Find the equation of the line that is:

  • parallel to y = 2x + 1
  • and passes though the point (5,4)

The slope of y = 2x + 1 is 2

The parallel line needs to have the same slope of 2.

We can solve it by using the "point-slope" equation of a line :

y − y 1 = 2(x − x 1 )

And then put in the point (5,4):

y − 4 = 2(x − 5)

That is an answer!

But it might look better in y = mx + b form. Let's expand 2(x − 5) and then rearrange:

y − 4 = 2x − 10

Vertical Lines

But this does not work for vertical lines ... I explain why at the end.

Not The Same Line

Be careful! They may be the same line (but with a different equation), and so are not parallel .

How do we know if they are really the same line? Check their y-intercepts (where they cross the y-axis) as well as their slope:

Example: is y = 3x + 2 parallel to y − 2 = 3x ?

For y = 3x + 2 : the slope is 3, and y-intercept is 2

For y − 2 = 3x : the slope is 3, and y-intercept is 2

So they are the same line and so are not parallel

Perpendicular Lines

Two lines are perpendicular when they meet at a right angle (90°).

To find a perpendicular slope:

When one line has a slope of m , a perpendicular line has a slope of −1 m

In other words the negative reciprocal

Find the equation of the line that is

  • perpendicular to y = −4x + 10
  • and passes though the point (7,2)

The slope of y = −4x + 10 is −4

The negative reciprocal of that slope is:

m = −1 −4 = 1 4

So the perpendicular line will have a slope of 1/4:

y − y 1 = (1/4)(x − x 1 )

And now we put in the point (7,2):

y − 2 = (1/4)(x − 7)

That answer is OK, but let's also put it in "y=mx+b" form:

y − 2 = x/4 − 7/4

y = x/4 + 1/4

Quick Check of Perpendicular

When we multiply a slope m by its perpendicular slope −1 m we get simply −1 .

So to quickly check if two lines are perpendicular:

When we multiply their slopes, we get −1

Are these two lines perpendicular?

When we multiply the two slopes we get:

2 × (−0.5) = −1

Yes, we got −1, so they are perpendicular.

The previous methods work nicely except for a vertical line :

In this case the gradient is undefined (as we cannot divide by 0 ):

m = y A − y B x A − x B = 4 − 1 2 − 2 = 3 0 = undefined

So just rely on the fact that:

  • a vertical line is parallel to another vertical line.
  • a vertical line is perpendicular to a horizontal line (and vice versa).
  • parallel lines: same slope
  • perpendicular lines: negative reciprocal slope (−1/m)

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Year 3 Parallel and Perpendicular Maths Challenge

Year 3 Parallel and Perpendicular Challenge

This Year 3 Parallel and Perpendicular Maths Challenge checks children’s understanding of parallel and perpendicular lines in a problem solving context. Children will match the descriptions of the shapes to each child.

If you would like to access  additional resources which link to this maths challenge, you can purchase a subscription for only £5.31 per month on our sister site, Classroom Secrets .

Teacher Specific Information

This Year 3 Parallel and Perpendicular Maths Challenge checks pupils’ understanding of parallel and perpendicular lines in a problem solving context. Pupils will match the descriptions of the shapes to each child.

National Curriculum Objectives

Properties of Shapes Mathematics Year 3: (3G2) Identify horizontal and vertical lines and pairs of perpendicular and parallel lines

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Mathematics LibreTexts

3.6: Parallel and Perpendicular Lines

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  • Page ID 18345

Learning Objectives

  • Determine the slopes of parallel and perpendicular lines.
  • Find equations of parallel and perpendicular lines

Definition of Parallel and Perpendicular

Parallel lines are lines in the same plane that never intersect. Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are parallel if their slopes are the same, \(m_{1}=m_{2}\). Consider the following two lines:

Consider their corresponding graphs:

Screenshot (628).png

Figure \(\PageIndex{1}\)

Both lines have a slope \(m=\frac{3}{4}\) and thus are parallel.

Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees). Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are perpendicular if the product of their slopes is \(−1: m1⋅m2=−1\). We can solve for \(m_{1}\) and obtain \(m_{1}=\frac{−1}{m_{2}}\). In this form, we see that perpendicular lines have slopes that are negative reciprocals , or opposite reciprocals. For example, if given a slope

\(m=-\frac{5}{8}\)

then the slope of a perpendicular line is the opposite reciprocal:

\(m_{\perp}=\frac{8}{5}\)

The mathematical notation \(m_{⊥}\) reads “\(m\) perpendicular.” We can verify that two slopes produce perpendicular lines if their product is \(−1\).

\(m\cdot m_{\perp}=-\frac{5}{8}\cdot\frac{8}{5}=-\frac{40}{40}=-1\quad\color{Cerulean}{\checkmark}\)

Geometrically, we note that if a line has a positive slope, then any perpendicular line will have a negative slope. Furthermore, the rise and run between two perpendicular lines are interchanged.

Screenshot (629).png

Figure \(\PageIndex{2}\)

Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign. In other words,

If \(m=\frac{a}{b}\), then \(m_{\perp}=-\frac{b}{a}\)

Determining the slope of a perpendicular line can be performed mentally. Some examples follow

Example \(\PageIndex{1}\)

Determine the slope of a line parallel to \(y=−5x+3\).

Since the given line is in slope-intercept form, we can see that its slope is \(m=−5\). Thus the slope of any line parallel to the given line must be the same, \(m_{∥}=−5\). The mathematical notation \(m_{∥}\) reads “\(m\) parallel.”

\(m_{∥}=−5\)

Example \(\PageIndex{2}\)

Determine the slope of a line perpendicular to \(3x−7y=21\).

First, solve for \(y\) and express the line in slope-intercept form.

In this form, we can see that the slope of the given line is \(m=\frac{3}{7}\), and thus \(m_{⊥}=−\frac{7}{3}\).

\(m_{⊥}=−\frac{7}{3}\)

Exercise \(\PageIndex{1}\)

Find the slope of the line perpendicular to \(15x+5y=20\).

\(m_{\perp}=\frac{1}{3}\)

Finding Equations of Parallel and Perpendicular Lines

We have seen that the graph of a line is completely determined by two points or one point and its slope. Often you will be asked to find the equation of a line given some geometric relationship—for instance, whether the line is parallel or perpendicular to another line.

Example \(\PageIndex{3}\)

Find the equation of the line passing through \((6, −1)\) and parallel to \(y=\frac{1}{2}x+2\)

Here the given line has slope \(m=\frac{1}{2}\), and the slope of a line parallel is \(m_{∥}=\frac{1}{2}\). Since you are given a point and the slope, use the point-slope form of a line to determine the equation.

\(\begin{array}{cc}{\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(6,-1)}&{m_{\parallel}=\frac{1}{2}} \end{array}\)

\(y=\frac{1}{2}x-4\)

It is important to have a geometric understanding of this question. We were asked to find the equation of a line parallel to another line passing through a certain point.

Screenshot (630).png

Figure \(\PageIndex{3}\)

Through the point \((6, −1)\) we found a parallel line, \(y=\frac{1}{2}x−4\), shown dashed. Notice that the slope is the same as the given line, but the \(y\)-intercept is different. If we keep in mind the geometric interpretation, then it will be easier to remember the process needed to solve the problem.

Example \(\PageIndex{4}\)

Find the equation of the line passing through \((−1, −5)\) and perpendicular to \(y=−\frac{1}{4}x+2\).

The given line has slope \(m=−\frac{1}{4}\), and thus \(m_{⊥}=+\frac{4}{1}=4\). Substitute this slope and the given point into point-slope form.

\(\begin{array}{cc} {\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(-1,-5)}&{m_{\perp}=4}\end{array}\)

Geometrically, we see that the line \(y=4x−1\), shown dashed below, passes through \((−1, −5)\) and is perpendicular to the given line.

Screenshot (631).png

Figure \(\PageIndex{4}\)

It is not always the case that the given line is in slope-intercept form. Often you have to perform additional steps to determine the slope. The general steps for finding the equation of a line are outlined in the following example.

Example \(\PageIndex{5}\)

Find the equation of the line passing through \((8, −2)\) and perpendicular to \(6x+3y=1\).

Step 1 : Find the slope \(m\). First, find the slope of the given line. To do this, solve for \(y\) to change standard form to slope-intercept form, \(y=mx+b\).

\(\begin{aligned} 6x+3y&=1 \\ 6x+3y\color{Cerulean}{-6x}&=1\color{Cerulean}{-6x} \\ 3y&=-6x+1 \\ \frac{3y}{\color{Cerulean}{3}}&=\frac{-6x+1}{\color{Cerulean}{3}} \\ y&=\frac{-6x}{3}+\frac{1}{3}\\y&=-2x+\frac{1}{3} \end{aligned}\)

In this form, you can see that the slope is \(m=−2=−\frac{2}{1}\), and thus \(m_{⊥}=\frac{−1}{−2}=+\frac{1}{2}\).

Step 2 : Substitute the slope you found and the given point into the point-slope form of an equation for a line. In this case, the slope is \(m_{⊥}=\frac{1}{2}\) and the given point is \((8, −2)\).

\(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-(-2)&=\frac{1}{2}(x-8) \end{aligned}\)

Step 3 : Solve for \(y\).

\(y=\frac{1}{2}x−6\)

Example \(\PageIndex{6}\)

Find the equation of the line passing through \((\frac{7}{2}, 1)\) and parallel to \(2x+14y=7\).

Find the slope \(m\) by solving for \(y\).

\(\begin{aligned} 2x+14y&=7 \\ 2x+14y\color{Cerulean}{-2x}&=7\color{Cerulean}{-2x} \\ 14y&=-2x+7 \\ \frac{14y}{\color{Cerulean}{14}}&=\frac{-2x+7}{\color{Cerulean}{14}} \\ y&=\frac{-2x}{14}+\frac{7}{14} \\ y&=-\frac{1}{7}x+\frac{1}{2} \end{aligned}\)

The given line has the slope \(m=−\frac{1}{7}\), and so \(m_{∥}=−\frac{1}{7}\). We use this and the point \((\frac{7}{2}, 1)\) in point-slope form.

\(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-1&=-\frac{1}{7}\left(x-\frac{7}{2} \right) \\ y-1&=-\frac{1}{7}x+\frac{1}{2} \\ y-1\color{Cerulean}{+1}&=-\frac{1}{7}x+\frac{1}{2}\color{Cerulean}{+1} \\ y&=-\frac{1}{7}x+\frac{1}{2}+\color{Cerulean}{\frac{2}{2}} \\ y&=-\frac{1}{7}x+\frac{3}{2} \end{aligned}\)

\(y=-\frac{1}{7}x+\frac{3}{2}\)

Exercise \(\PageIndex{2}\)

Find the equation of the line perpendicular to \(x−3y=9\) and passing through \((−\frac{1}{2}, 2)\).

\(y=-3x+\frac{1}{2}\)

When finding an equation of a line perpendicular to a horizontal or vertical line, it is best to consider the geometric interpretation.

Example \(\PageIndex{7}\)

Find the equation of the line passing through \((−3, −2)\) and perpendicular to \(y=4\).

We recognize that \(y=4\) is a horizontal line and we want to find a perpendicular line passing through \((−3, −2)\).

Screenshot (632).png

Figure \(\PageIndex{5}\)

If we draw the line perpendicular to the given horizontal line, the result is a vertical line.

Screenshot (633).png

Figure \(\PageIndex{6}\)

Equations of vertical lines look like \(x=k\). Since it must pass through \((−3, −2)\), we conclude that \(x=−3\) is the equation. All ordered pair solutions of a vertical line must share the same \(x\)-coordinate.

\(x=−3\)

We can rewrite the equation of any horizontal line, \(y=k\), in slope-intercept form as follows:

Written in this form, we see that the slope is \(m=0=\frac{0}{1}\). If we try to find the slope of a perpendicular line by finding the opposite reciprocal, we run into a problem: \(m_{⊥}=−\frac{1}{0}\), which is undefined. This is why we took care to restrict the definition to two nonvertical lines. Remember that horizontal lines are perpendicular to vertical lines.

Key Takeaways

  • Parallel lines have the same slope.
  • Perpendicular lines have slopes that are opposite reciprocals. In other words, if \(m=\frac{a}{b}\), then \(m_{⊥}=−\frac{b}{a}\).
  • To find an equation of a line, first use the given information to determine the slope. Then use the slope and a point on the line to find the equation using point-slope form.
  • Horizontal and vertical lines are perpendicular to each other.

Exercise \(\PageIndex{3}\) Parallel and Perpendicular Lines

Determine the slope of parallel lines and perpendicular lines.

  • \(y=−\frac{3}{4}x+8\)
  • \(y=\frac{1}{2}x−3\)
  • \(y=−3x+7\)
  • \(y=−\frac{5}{8}x−12\)
  • \(y=\frac{7}{3}x+\frac{3}{2}\)
  • \(y=9x−25\)
  • \(y=−10x+15\)
  • \(x=−12\)
  • \(x−y=0\)
  • \(4x+3y=0\)
  • \(3x−5y=10\)
  • \(−2x+7y=14\)
  • \(−x−y=\frac{1}{5}\)
  • \(\frac{1}{2}x−\frac{1}{3}y=−1\)
  • \(−\frac{2}{3}x+\frac{4}{5}y=8\)
  • \(2x−\frac{1}{5}y=\frac{1}{10}\)
  • \(−\frac{4}{5}x−2y=7\)

1. \(m_{∥}=−\frac{3}{4}\) and \(m_{⊥}=\frac{4}{3}\)

3. \(m_{∥}=4\) and \(m_{⊥}=−\frac{1}{4}\)

5. \(m_{∥}=−\frac{5}{8}\) and \(m_{⊥}=\frac{8}{5}\)

7. \(m_{∥}=9\) and \(m_{⊥}=−\frac{1}{9}\)

9. \(m_{∥}=0\) and \(m_{⊥}\) undefined

11. \(m_{∥}=1\) and \(m_{⊥}=−1\)

13. \(m_{∥}=−\frac{4}{3}\) and \(m_{⊥}=\frac{3}{4}\)

15. \(m_{∥}=\frac{2}{7}\) and \(m_{⊥}=−\frac{7}{2}\)

17. \(m_{∥}=\frac{3}{2}\) and \(m_{⊥}=−\frac{2}{3}\)

19. \(m_{∥}=10\) and \(m_{⊥}=−\frac{1}{10}\)

Exercise \(\PageIndex{4}\) Parallel and Perpendicular Lines

Determine if the lines are parallel, perpendicular, or neither.

  • \(\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x−3\end{aligned}\right.\)
  • \(\left\{\begin{aligned}y&=\frac{3}{4}x−1\\y&=\frac{4}{3}x+3\end{aligned}\right.\)
  • \(\left\{\begin{aligned}y&=−2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.\)
  • \(\left\{\begin{aligned}y&=3x−\frac{1}{2}\\ y&=3x+2\end{aligned}\right.\)
  • \(\left\{\begin{aligned}y&=5\\x&=−2\end{aligned}\right.\)
  • \(\left\{\begin{aligned}y&=7\\y&=−\frac{1}{7}\end{aligned}\right.\)
  • \(\left\{\begin{aligned}3x−5y&=15\\ 5x+3y&=9\end{aligned}\right.\)
  • \(\left\{\begin{aligned}x−y&=7\\3x+3y&=2\end{aligned}\right.\)
  • \(\left\{\begin{aligned}2x−6y&=4\\−x+3y&=−2 \end{aligned}\right.\)
  • \(\left\{\begin{aligned}−4x+2y&=3\\6x−3y&=−3 \end{aligned}\right.\)
  • \(\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.\)
  • \(\left\{\begin{aligned}y−10&=0\\x−10&=0 \end{aligned}\right.\)
  • \(\left\{\begin{aligned}y+2&=0\\2y−10&=0 \end{aligned}\right.\)
  • \(\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.\)
  • \(\left\{\begin{aligned}−5x+4y&=20\\10x−8y&=16 \end{aligned}\right.\)
  • \(\left\{\begin{aligned}\frac{1}{2}x−\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=−2\end{aligned}\right.\)

1. Parallel

3. Perpendicular

5. Perpendicular

7. Perpendicular

9. Parallel

11. Neither

13. Parallel

15. Parallel

Exercise \(\PageIndex{5}\) Equations in Point-Slope Form

Find the equation of the line

  • Parallel to \(y=\frac{1}{2}x+2\) and passing through \((6, −1)\).
  • Parallel to \(y=−\frac{3}{4}x−3\) and passing through \((−8, 2)\).
  • Perpendicular to \(y=3x−1\) and passing through \((−3, 2)\).
  • Perpendicular to \(y=−\frac{1}{3}x+2\) and passing through \((4, −3)\).
  • Perpendicular to \(y=−2\) and passing through \((−1, 5)\).
  • Perpendicular to \(x=\frac{1}{5}\) and passing through \((5, −3)\).
  • Parallel to \(y=3\) and passing through \((2, 4)\).
  • Parallel to \(x=2\) and passing through (7, −3)\).
  • Perpendicular to \(y=x\) and passing through \((7, −13)\).
  • Perpendicular to \(y=2x+9\) and passing through \((3, −1)\).
  • Parallel to \(y=\frac{1}{4}x−5\) and passing through \((−2, 1)\).
  • Parallel to \(y=−\frac{3}{4}x+1\) and passing through \((4, \frac{1}{4})\).
  • Parallel to \(2x−3y=6\) and passing through \((6, −2)\).
  • Parallel to \(−x+y=4\) and passing through \((9, 7)\).
  • Perpendicular to \(5x−3y=18\) and passing through \((−9, 10)\).
  • Perpendicular to \(x−y=11\) and passing through \((6, −8)\).
  • Parallel to \(\frac{1}{5}x−\frac{1}{3}y=2\) and passing through \((−15, 6)\).
  • Parallel to \(−10x−\frac{5}{7}y=12\) and passing through \((−1, \frac{1}{2})\).
  • Perpendicular to \(\frac{1}{2}x−\frac{1}{3}y=1\) and passing through \((−10, 3)\).
  • Perpendicular to \(−5x+y=−1\) and passing through \((−4, 0)\).
  • Parallel to \(x+4y=8\) and passing through \((−1, −2)\).
  • Parallel to \(7x−5y=35\) and passing through \((2, −3)\).
  • Perpendicular to \(6x+3y=1\) and passing through \((8, −2)\).
  • Perpendicular to \(−4x−5y=1\) and passing through \((−1, −1)\).
  • Parallel to \(−5x−2y=4\) and passing through \((\frac{1}{5}, −\frac{1}{4})\).
  • Parallel to \(6x−\frac{3}{2}y=9\) and passing through \((\frac{1}{3}, \frac{2}{3})\).
  • Perpendicular to \(y−3=0\) and passing through \((−6, 12)\).
  • Perpendicular to \(x+7=0\) and passing through \((5, −10)\).

1. \(y=\frac{1}{2}x−4\)

3. \(y=−\frac{1}{3}x+1\)

5. \(x=−1\)

9. \(y=−x−6\)

11. \(y=\frac{1}{4}x+\frac{3}{2}\)

13. \(y=\frac{2}{3}x−6\)

15. \(y=−\frac{3}{5}x+\frac{23}{5}\)

17. \(y=\frac{3}{5}x+15\)

19. \(y=−\frac{2}{3}x−\frac{11}{3}\)

21. \(y=−\frac{1}{4}x−\frac{9}{4}\)

23. \(y=\frac{1}{2}x−6\)

25. \(y=−\frac{5}{2}x+\frac{1}{4}\)

27. \(x=−6\)

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Parallel and Perpendicular Lines (graphs) Practice Questions

Parallel lines    questions     answers, perpendicular lines    questions     answers.

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Parallel and Perpendicular Lines With Word Problems

Parallel and perpendicular lines, parallel lines:.

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.

parallel and perpendicular lines problem solving year 3

Real-life Example:

Real Life Example

Perpendicular Lines:

Perpendicular lines are lines that intersect at a right (90-degree) angle.

Perpendicular Lines

Classify Lines

Example1:   

Are the graph of the equations y= -1/7 x-5 and y=-1/7 x-1 parallel, perpendicular, or neither?

parallel

Identify the slope of each line.

 y= -1/7 x-5                   y=-1/7 x-1

m 1 = -1/7                      m 2 = -1/7                                 

Compare the slope of the lines .

The slopes of the lines are -1/7 and –1/7.          

The slope is the same.

Parallel Lines have the same slope

The graph of the equations and y= -1/7 x-5 and y=-1/7 x-1 are parallel.

Example2:   

Is the graph of the equations x+2y=7 and -2x+y=3 parallel, perpendicular, or neither?

First line:                                                     

x+2y=7         

Divided both sides by 2.

parallel and perpendicular lines problem solving year 3

m=-1/2                                                           

Second line:           

  y =2x +3     

The slopes of the lines are – 1/2 and 2.

Compare the slope of the lines.

The slopes of the lines – 1/2  and 2 are opposite and reciprocals

perpendicular.

Solve Real Word Problems

Architecture, An architect uses software to design the ceiling of a room. The architect needs to enter an equation that represents a new beam. The new beam will be perpendicular to the existing beam, which is represented by the red line. The new beam will pass through the corner represented by the blue point. What is the equation that represents the new beam?

Existing Beam

Use the slope formula to find the slope of the red line that represents the existing beam.

The slope of the line that represents the existing beam is = – 2/3.

Find the opposite reciprocal of the slope from step 1.

The opposite reciprocal is -2/3  is 3/2

Use the point-slope form to write an equation. The slope of the line that represents the new beam is 3/2.

It will pass through (12, 10)

An equation that represents the new beam is

  • Are the graphs of the equations parallel, perpendicular, or neither?

a. x-3y =6 and x-3y =9

b. y=4x+1 and y=-4x -2

2. How many types of lines are there?

3. Determine that the lines are parallel, perpendicular, or neither.

2x-3y =9 and 6y-4x=1

4. Identify the below shape as parallel, perpendicular, or neither.

Shape as Parallel

5. Identify the lines as parallel or perpendicular.

     2x+5y =7

     4x+10y =18

6. How do you identify parallel lines and perpendicular lines?

7. Do parallel lines meet?

8. What are some examples of perpendicular lines in real life?

9. When put on a coordinate plane, Main Street has the equation y = – 1/3 x-4 Park Street is perpendicular to Main Street and goes through the point (3, -5). Write the equation for Park Street in slope-intercept form.

10. You and your friend have gift cards to a shopping mall. Your card has $20 on it, and your friend’s card has $30 on it. For every month that you don’t use your card, its value decreases by $2. Write two equations modeling your and your friend’s gift cards, then determine if the lines are parallel or perpendicular.

       Concept Map:

Concept Map

What We Have Learned:

  • Understand parallel and perpendicular lines
  • Classify lines
  • Solve real word problems
  • Identify parallel and perpendicular lines in real life.

Parallel and Perpendicular Lines

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IMAGES

  1. Year 3 Parallel and Perpendicular Lesson

    parallel and perpendicular lines problem solving year 3

  2. Problem Solving to Find the Equation of Parallel and Perpendicular

    parallel and perpendicular lines problem solving year 3

  3. 10++ Slopes Of Parallel And Perpendicular Lines Worksheet

    parallel and perpendicular lines problem solving year 3

  4. 41 parallel lines and perpendicular lines worksheet

    parallel and perpendicular lines problem solving year 3

  5. Year 3

    parallel and perpendicular lines problem solving year 3

  6. 6 3 Write Equations Of Parallel And Perpendicular Lines Worksheet

    parallel and perpendicular lines problem solving year 3

VIDEO

  1. Parallel & Perpendicular Lines

  2. 3.5 Equations of Parallel and Perpendicular Lines

  3. Conditions for lines to be parallel or perpendicular

  4. Parallel & perpendicular lines 10 min

  5. 6.4 Parallel and Perpendicular Lines (Grade 9 Academic MPM1D)

  6. Parallel and Perpendicular Line Problems (Simplifying Math)

COMMENTS

  1. PDF Year 3 Parallel and Perpendicular Reasoning and Problem Solving

    Year 3 Parallel and Perpendicular Reasoning and Problem Solving Reasoning and Problem Solving Step 6: Parallel and Perpendicular National Curriculum Objectives: Mathematics Year 3: (3G2) Identify horizontal and vertical lines and pairs of perpendicular and parallel lines Differentiation:

  2. Parallel and Perpendicular Lines Year 3

    Year 3 Parallel and Perpendicular Lines (KS2) resource Use these differentiated worksheets to help KS2 children practise identifying parallel and perpendicular lines in year 3 and to consolidate what they have learned in their Maths lessons. Show more Related Searches

  3. Year 3 Mastery: Parallel and Perpendicular Teaching Pack

    With fluency, reasoning, and problem-solving questions and tasks, this easy-to-use pack will help your teaching on the White Rose Summer Block: Properties of Shape, specifically White Rose small step: 'parallel and perpendicular'.

  4. Year 3 Parallel and Perpendicular Lesson

    This Year 3 Parallel and Perpendicular lesson covers the prior learning of right angles in shapes, before moving onto the main skill of parallel and perpendicular lines. The lesson starts with a prior learning worksheet to check pupils' understanding. The interactive lesson slides recap the prior learning before moving on to the main skill.

  5. Y3 Identify Parallel and Perpendicular Lines

    It meets the year 3 national curriculum aim for properties of shapes 'Identify horizontal and vertical lines and pairs of perpendicular and parallel lines'. This is the second in a block of two lessons on different types of lines. What is meant by parallel and perpendicular lines? Parallel lines are always the same distance apart.

  6. Teaching Year 3 Perpendicular and Parallel Lines Help

    In this video, Twinkl Teacher Saleena's fantastic Year 3 perpendicular and parallel lines video lesson is previewed where children how to explain, define and...

  7. Parallel and Perpendicular Lines Year 3

    Year 3 Parallel and Perpendicular Lines (KS2) resource. Use these differentiated worksheets to help KS2 children practise identifying parallel and perpendicular lines in year 3 and to consolidate what they have learned in their Maths lessons.. Containing 6 worksheets on parallel and perpendicular lines for KS2, this pack starts with simple worksheets which ask pupils to circle the examples of ...

  8. Year 3 Parallel and Perpendicular Lines

    Year 3 Parallel and Perpendicular Lines. Carroll diagram worksheet (lines of symmetry and parallel or perpendicular) Buy / Subscribe. 20p. FREE. Parallel and perpendicular lines lesson plan. Parallel and perpendicular lines powerpoint. Buy / Subscribe.

  9. Perpendicular and Parallel Lines Worksheet

    Each perpendicular and parallel lines worksheet has been designed to help children in Year 3 consolidate what they have learnt in Maths lessons. This pack contains 6 different worksheets on parallel and perpendicular lines. The starter worksheets task your students with identifying examples of parallel and perpendicular lines.

  10. Year 3 Parallel and Perpendicular Lines Worksheet

    Parallel and perpendicular lines worksheet for Year 3 angle and shape topic. This time-saving worksheet is designed to be used alongside White Rose Maths home learning activities for the summer term 2020. It provides opportunities for pupils to independently practise what they've been learning, especially when parents aren't able to support directly or where pupils don't have access to the ...

  11. IXL

    out of 100 IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more 0 Work it out

  12. Parallel and Perpendicular Lines (Year 3)

    Last Updated: 24/10/2023 Resource Code: M2WAE55 Curriculum Point (s): Identify horizontal and vertical lines and pairs of perpendicular and parallel lines. Parallel and Perpendicular Lines in Shapes (Year 3) Properties of Shapes Key Stage 2 Maths Parallel and Perpendicular Lines (Year 3)

  13. Parallel, Perpendicular and Intersecting Lines Worksheets

    A variety of pdf exercises and word problems will help improve the skills of students in grade 3 through grade 8 to identify and differentiate between parallel, perpendicular and intersecting lines. ... or finding out the number of parallel and perpendicular lines, these printable worksheets for grade 4, grade 5, and grade 6 have both the ...

  14. Parallel and Perpendicular Lines (Year 3)

    Parallel and Perpendicular Lines (Year 3) Author: Andrew Lochery Save to Your Lessons Save to Homework Share resource If children need more practice on parallel and perpendicular lines, this worksheet is a great way to consolidate and extend their learning.

  15. Finding Parallel and Perpendicular Lines

    The parallel line needs to have the same slope of 2. We can solve it by using the "point-slope" equation of a line: y − y1 = 2 (x − x1) And then put in the point (5,4): y − 4 = 2 (x − 5) That is an answer! But it might look better in y = mx + b form. Let's expand 2 (x − 5) and then rearrange: y − 4 = 2x − 10.

  16. Year 3 Parallel and Perpendicular Maths Challenge

    This Year 3 Parallel and Perpendicular Maths Challenge checks pupils' understanding of parallel and perpendicular lines in a problem solving context. Pupils will match the descriptions of the shapes to each child.

  17. 3.6: Parallel and Perpendicular Lines

    3: Graphing Lines 3.6: Parallel and Perpendicular Lines

  18. Parallel and Perpendicular Lines (graphs) Practice Questions

    Perpendicular Lines Questions Answers. . Practice Questions. Previous: Gradient Practice Questions. Next: Multiplication Practice Questions. The Corbettmaths Practice Questions on Parallel lines and perpendicular lines.

  19. Parallel & perpendicular lines from equation

    Perpendicular lines from equation. Parallel & perpendicular lines from equation. Writing equations of perpendicular lines. Writing equations of perpendicular lines (example 2) Write equations of parallel & perpendicular lines. Proof: parallel lines have the same slope. Proof: perpendicular lines have opposite reciprocal slopes.

  20. PDF PARALLEL AND PERPENDICULAR LINES PRACTICE QUESTIONS

    (b) Circle the equation of the line that is perpendicular to L. y = 3x + 11 y = 2x + 3 y = - 1 2 x + 9 y = 1 2 x - 5 3. Line A has equation y = 3 2 x + 9. (a) Circle the equation of the line that is parallel to A. y = 2x + 5 y = - 3 2 x + 13 y = - 2 3 x + 11 y = 3 2 x - 2 (b) Circle the equation of the line that is perpendicular to A.

  21. Parallel and Perpendicular Lines

    In this problem, we are going to have two answers. One answer is the line that is parallel to the reference line and passing through a given point. Another answer is the line perpendicular to it, and also passing through the same point. Part 1: Determine the parallel line using the slope [latex]m = {2 \over 5} [/latex] and the point [latex ...

  22. Parallel and Perpendicular Lines With Word Problems

    Are the graphs of the equations parallel, perpendicular, or neither? a. x-3y =6 and x-3y =9. b. y=4x+1 and y=-4x -2. 2. How many types of lines are there? 3. Determine that the lines are parallel, perpendicular, or neither. 2x-3y =9 and 6y-4x=1. 4. Identify the below shape as parallel, perpendicular, or neither.