Cambridge International Mathematics

Coordinate geometry (Chapter 12) 263

2 Find the coordinates of the midpoint of the line segment joining the pairs of points:

a (8,1)and(2,5) b (2,¡3)and(0,1) c (3,0)and(0,6)

d (¡ 1 ,4)and(1,4) e (5,¡3)and(¡ 1 ,0) f (¡ 2 ,4)and(4,¡2)

g (5,9)and(¡ 3 ,¡4) h (3,¡2)and(1,¡5)

3 M is the midpoint of AB. Find the coordinates of B for:

a A(6,4)and M(3,¡1) b A(¡ 5 ,0)and M(0,¡1) c A(3,¡2)and M(1^12 ,2)

d A(¡ 1 ,¡2)and M(¡^12 , 212 ) e A(7,¡3)and M(0,0) f A(3,¡1)and M(0,¡^12 )

Check your answers using theequal stepsmethod given inExample 10.

4 If T is the midpoint of PQ, find the coordinates of P for:

a T(¡ 3 ,4)and Q(3,¡2) b T(2,0)and Q(¡ 2 ,¡3).

5 AB is the diameter of a circle with centre C. If A is(3,¡2)and B is (¡ 1 ,¡4), find the coordinates

of C.

6 PQ is a diameter of a circle with centre (3,¡^12 ). Find the coordinates of P given that Q is (¡ 1 ,2).

7 The diagonals of parallelogram PQRS bisect each other at X.

Find the coordinates of S.

8 Triangle ABC has vertices A(¡ 1 ,3),B( 1 ,¡1), and C(5,2).

Find the length of the line segment from A to the midpoint of

BC.

9 A, B, C and D are four points on the same straight line. The

distances between successive points are equal, as shown. If A

is (1,¡3),Cis(4,a) and D is (b,5), find the values of

aandb.

When looking at line segments drawn on a set of axes, it is clear that different line segments are inclined to

the horizontal at different angles. Some appear to besteeperthan others.

Thegradientof a line is a measure of its steepness.

If we choose any two distinct (different) points on the line, thehorizontal stepandvertical stepbetween

them may be determined.

Case 1: Case 2:

D GRADIENT OF A LINE SEGMENT [7.1, 7.4]

horizontal step

positive

vertical step

horizontal step

negative

vertical step

P,()0 ¡3

R,()3 ¡0

Q,()5 ¡3

X

S

A

B

C

D

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y:\HAESE\IGCSE01\IG01_12\263IGCSE01_12.CDR Thursday, 25 September 2008 10:55:52 AM PETER