Perpendicular lines are lines which cross at a right angle.

If the gradient of a line is m, then the gradient of a perpendicular line is .

When we multiply the gradients of two perpendicular lines, we get an answer of -1.

Example 1

Find the gradient of a line which is perpendicular to a line with gradient:

a) 3

b) -1/4

c) 1.5

Answers

a) 3 × -1/3 = -1, so the gradient is =1/3

b) -1/4 × 4 = -1, so the gradient is 4

c) 1.5 × -2/3 = -1, so the gradient is -2/3

Example 2

Find the gradient of a line which is perpendicular to 2y = 6x - 1.

Answer

You need to rearrange the equation into the form y = mx + c. m will be the gradient

2y = 6x - 1

y = 3x - 1/2

The gradient of this line is 3.

The gradient of the perpendicular line is -1/3, because 3 × -1/3 = -1.