### 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:

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