 # Gradients of Parallel and Perpendicular Lines

In this worksheet, students answer questions using the relationship between the gradients of parallel and perpendicular lines. Key stage:  KS 3

Curriculum topic:   Algebra

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

Difficulty level:   ### 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.

Invert the fraction and multiply by -1.

 3 → 4 → -4 4 3 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.

6
12/2
• Question 2

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

1/3
-3
• Question 3

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

1/4
-12/3
• Question 4

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

1/4
2/8
• Question 5

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

2/3
4/6
• Question 6

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

2/3
-1.5
• Question 7

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

-1
1
• Question 8

The gradients of 4 lines are shown.

Select a pair of gradients which would represent perpendicular lines.

4/5
-1¼
• Question 9

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

-4
-8/2
• Question 10

The gradients of 4 lines are shown.

Select a pair of gradients which would represent parallel lines.

9/4

---- OR ----

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