Perpendicular Lines

What is to be learned?

• The rule connecting gradients and perpendicular lines.

x

y

(2, 2)

(7 , 6)

m = 6 – 2

7 – 2= 4/5

(-2 , 7)

m = 7 – 2

-2 – 2= - 5/4

m1

m2

x

y

(1, 3)

(8 , 5)

m = 5 – 3

8 – 1= 2/7

(-1 , 10)

m = 10 – 3

-1 – 1= - 7/2

m1

m2

Summarising

m1 m2

4/5

2/7

-9/11

4

-5/4

-7/2

11/9

1 - ¼

4/5 X -5/4 = - 20/20= -1

m1m2 = -1

For perpendicular lines

m1m2 = -1

If AB is ppdlr to CD

Ex 1 mAB = 6/7

Ex 2 mAB = - 3/8

Ex 3 mAB = 5

mAB = 0!!!

mCD = - 7/6

mCD = 8/3

(5/1) mCD = - 1/5

mCD = ∞

Parallel and Perpendicular

Which lines are perpendicular

Which lines are parallel?

y = 4x + 7 y = ½x +2

y = ¼x y = – 5 + 4x

y = -2x + 4 y = 2x – 4