Perpendicular Linesa) Work out the gradient of the line ABb) Draw a line which is perpendicular to the line AB.c) Hence work out the gradient of the perpendicular line

A

B

0 2 4 6 8

2

x

y

4

-2

a) Work out the gradient of the line LMb) Draw a line which is perpendicular to the line LM.c) Hence work out the gradient of the perpendicular line

L

M

0 2 4 6 8

2

x

y

4

-2

If two lines are perpendicular to each other with gradients m1 and m2 then it is true to say

m1

m2

21

1

mm

121 mm

or

Example

Find the equation of the line which passes through (2, 3) which is

a) Parallel to the line

b) Perpendicular to the line

43 xy32 xy

Example

Obtain the equation of the perpendicular bisector of AB where A has coordinate (–1, 4) and B has coordinate (5, 6)