Cambridge International Mathematics

Challenge

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274 Coordinate geometry (Chapter 12)

1 Triangle ABC sits on thex-axis so that vertices A and

B are equidistant from O.

a Find the length of AC.

b Find the length of BC.

c If AC=BC, deduce that ab=0.

d Copy and complete the following statement based

on the result ofc.

“The perpendicular bisector of the base of an

isosceles triangle ......”

2 OABC is a parallelogram. You may assume that the

opposite sides of the parallelogram are equal in length.

a Find the coordinates of B.

b Find the midpoints of AC and OB.

c What property of parallelograms has been deduced

inb?

3 By considering the figure alongside:

a Find the equations of the perpendicular bisectors

of OA and AB (these are the lines PS and SQ

respectively).

b Useato find thex-coordinate of S.

c Show that RS is perpendicular to OB.

d Copy and complete:

“The perpendicular bisectors of the sides of a

triangle ......”

x

y

B,()a¡0

C,()bc¡

A,()-¡0a O

x

y C,()bc¡ B

O A,()a¡0

A,()2¡2ac

R,()b¡0 B,()2¡0b

x

y

P Q

S

O

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y:\HAESE\IGCSE01\IG01_12\274IGCSE01_12.CDR Thursday, 23 October 2008 12:04:10 PM PETER