Perpendicular Lines - for GCSE, IGCSE, O Level & AS

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Perpendicular Lines GCSE, IGCSE, GCE OL maths

If two lines are perpendicular, the gradient of one line is the negative
reciprocal of the other line.

E.g.1

Find the equation of the perpendicular line to the equation, y = 2x - 3 that goes through the point (4,5).
The gradient of the perpendicular line = -1/2 = -0.5
For the perpendicular line,
m = -0.5 x = 4, y = 5
y = mx + c
5 = -0.5(4) + c
c = 7
y = -0.5x + 7
The equation of the perpendicular line, y = -0.5x + 7

E.g.2

Find the equation of the perpendicular line to the equation, y = 1/2x - 5 that goes through the point (2,-1).
The gradient of the perpendicular line = -1/(1/2) = -2
For the perpendicular line,
m = -2 x = 2, y = -1
y = mx + c
-2 = -2(2) + c
c = 2
y = -2x + 2
The equation of the perpendicular line, y = -2x + 2

E.g.3

Find the equation of the perpendicular line to the equation, y = -4x - 3 that goes through the point (8,1).
The gradient of the perpendicular line = -1/(-4) = 1/4
For the perpendicular line,
m = 1/4 x = 8, y = 1
y = mx + c
1 = 0.25(8) + c
c = -1
y = -1/4x - 1
The equation of the perpendicular line, y = -1/4x - 1

For interactive practice, please use the following applet:


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