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Recognise Parallel and Perpendicular Lines From Their Gradients

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

'Recognise Parallel and Perpendicular Lines From Their Gradients' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Algebra

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

Popular topics:   Algebra worksheets

Difficulty level:  

Worksheet Overview

Parallel lines have the same gradient.

All of these lines have a gradient of 5.

 

gradient of parallel lines

 

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

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

 

perpendicular lines

 

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

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