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

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: