This document discusses the rule for determining if two lines are perpendicular based on their gradients. It explains that for perpendicular lines, the product of their gradients (m1 and m2) equals -1. Several examples are provided of calculating the gradients of lines from points on each line and verifying that the lines are perpendicular when m1 × m2 = -1. The document also discusses how to determine if lines are parallel based on having equal gradients.

1. Block 1
Perpendicular Lines

2. What is to be learned?
• The rule connecting gradients and
perpendicular lines.

3. x
y
(2, 2)
(7 , 6)
m = 6 – 2
7 – 2
= 4
/5
(-2 , 7)
m = 7 – 2
-2 – 2
= - 5
/4
m1
m2

4. x
y
(1, 3)
(8 , 5)
m = 5 – 3
8 – 1
= 2
/7
(-1 , 10)
m = 10 – 3
-1 – 1
= - 7
/2
m1
m2

5. 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

6. 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 = ∞

7. 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