Cambridge International Mathematics

Coordinate geometry (Chapter 12) 265

THE GRADIENT FORMULA

If A is(x 1 ,y 1 )and B is(x 2 ,y 2 )then thegradientof

AB is

y 2 ¡y 1

x 2 ¡x 1

:

Example 12 Self Tutor

Find the gradient of the line through(3,¡2)and(6,4).

(3,¡2) (6,4)

x 1 y 1 x 2 y 2

gradient =

y 2 ¡y 1

x 2 ¡x 1

=

4 ¡¡ 2

6 ¡ 3

=^63

=2

Example 13 Self Tutor

Through(2,4)draw a line with gradient¡^23.

Plot the point(2,4)

gradient=

y-step

x-step

=

¡ 2

3

) lety-step=¡ 2 ,x-step=3.

Use these steps to find another

point and draw the line through

these points.

EXERCISE 12D.1

1 Find the gradient of

each line segment:

2 On grid paper draw a line segment with gradient:

a^34 b ¡^12 c 2 d ¡ 3 e 0 f ¡^25

y

x

y 1

x 1

y 2

x 2

A

B

yy 21 -

xx 21 -

O

y

x

()2 ¡4,

2

2

4

4

3

3

• 2
  
  
  • 2
  
  
  
  

b

f

c

g

d

h

a

e

It is a good

idea to use

a positive

x-step.

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y:\HAESE\IGCSE01\IG01_12\265IGCSE01_12.CDR Thursday, 25 September 2008 11:19:48 AM PETER