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Gradients of Parallel and Perpendicular Lines

In this worksheet, students answer questions using the relationship between the gradients of parallel and perpendicular lines.

'Gradients of Parallel and Perpendicular Lines' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

Curriculum subtopic:  Use Linear Equations (Two Variables) and Gradients

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Parallel lines have the same gradient.

All of these lines have a gradient of 5.

 

 

Perpendicular lines have gradients which multiply together to give -1.

Here one line has a gradient of 5 and the other of -1/5.

 

To find the gradient of a line which is perpendicular to one of gradient a/b, we invert the fraction and multiply by -1.

This means you don't need diagrams to check if lines are perpendicular.

 

 

Example

State the gradient of a line which is perpendicular to one of gradient ¾.

 

Answer

Invert the fraction and multiply by -1.

3 4 -4
4 3 3

  

Answer is -4
3

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

1/3

6

-3

12/2

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

1/3

6

-3

12/2

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

1/4

-3

2/8

-12/3

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

1/4

-3

2/8

-12/3

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

2/3

4/6

-1.5

-1/3

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

2/3


-1.5

-1/3

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

2


-1

1

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

-4

4/5

-1¼

4

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

-4

8/2

-1¼

-8/2

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

0

9/4

-1¼


  • Question 1

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

CORRECT ANSWER
6
12/2
  • Question 2

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

CORRECT ANSWER
1/3
-3
  • Question 3

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

CORRECT ANSWER
1/4
-12/3
  • Question 4

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

CORRECT ANSWER
1/4
2/8
  • Question 5

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

CORRECT ANSWER
2/3
4/6
  • Question 6

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

CORRECT ANSWER
2/3
-1.5
  • Question 7

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

CORRECT ANSWER
-1
1
  • Question 8

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

CORRECT ANSWER
4/5
-1¼
  • Question 9

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

CORRECT ANSWER
-4
-8/2
  • Question 10

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

CORRECT ANSWER
9/4

---- OR ----

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