Perpendicular lines - Intermediate and Higher tier - Equations of lines – WJEC - GCSE Maths Revision - WJEC

Perpendicular lines - Intermediate and Higher tier

Perpendicular lines will always cross at right angles.

To determine if two lines are perpendicular, we need to multiply their gradients together. If the lines are perpendicular to each other, the product of their gradients will be -1.

We say \({M_{1} \times~M_{2} = -1}\), where \({M_{1}}\) is the gradient of the first line and \({M_{2}}\) is the gradient of the second line.

A graph with two solid lines crossing at a right-angle. One line is labelled 'Gradient M1' and the other 'Gradient M2'.

Example

Are the lines \(\text{y = x - 5}\) and \(\text{y + x = 3}\) perpendicular to each other?

First we need to ensure both lines are in the form \(\text{y = mx + c}\).

Rearranging \(\text{y + x = 3}\) gives us \(\text{y = -x + 3}\).

So, \({M_{1} = 1}\) and \({M_{2} = -1}\).

\({M_{1} \times ~M_{2} = 1 \times -1 = -1}\).

So the lines are perpendicular.

Question

Are the lines \(\text{2y = x + 7}\) and \(\text{y + 2x = 3}\) perpendicular?

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Parallel lines - Intermediate and Higher tier

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Equations of lines – WJECPerpendicular lines - Intermediate and Higher tier