Cambridge International Mathematics

262 Coordinate geometry (Chapter 12)

Example 8 Self Tutor

Find the coordinates of the midpoint of AB for A(¡ 1 ,3)and B(4,7).

x-coordinate of midpoint

=

¡1+4

2

=^32

=1^12

y-coordinate of midpoint

=

3+7

2

=5

) the midpoint of AB is (1^12 ,5).

Example 9 Self Tutor

M is the midpoint of AB. Find the coordinates of B if A is(1,3)and M is(4,¡2).

Let B be(a,b)

)

a+1

2

=4 and

b+3

2

=¡ 2

) a+1=8 and b+3=¡ 4

) a=7 and b=¡ 7

) Bis(7,¡7).

Example 10 Self Tutor

Suppose A is(¡ 2 ,4)and M is(3,¡1), where M is the midpoint of AB.

Useequal stepsto find the coordinates of B.

x-step: ¡ 238

y-step: 4 ¡ 1 ¡ 6

) Bis(8,¡6).

EXERCISE 12C

1 Use this diagram only to find the coordinates of the

midpoint of the line segment:

a GA b ED

c AC d AD

e CD f GF

g EG h GD

You may also be able

to find the midpoint

from a sketch.

A (1, 3)

M (4, 2)-

B( , )ab

y

x

G

F

E

A

C

B

D

3

O 3

+5

+5

-5

-5

A,()-2 ¡4

M,()3 ¡-1

B,()8 -6

+5 +5

¡ 5 ¡ 5

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y:\HAESE\IGCSE01\IG01_12\262IGCSE01_12.CDR Friday, 3 October 2008 12:11:19 PM PETER