Cambridge International Mathematics

272 Coordinate geometry (Chapter 12)

5

a Find the coordinates of: i P ii Q iii R iv S.

b Find the gradient of: i PQ ii QR iii RS iv SP.

c What can be deduced about quadrilateral PQRS fromb?

6 S(6,a)lies on a semi-circle as shown.

a Finda.

b Using this value ofa, find the gradient of:

i AC ii CB.

c Usebto show that angle ACB is a right angle.

Review set 12A

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1 Plot the following points on the number plane:

A(1,3) B(¡ 2 ,0) C(¡ 2 ,¡3) D(2,¡1)

2 Find the distance between the following sets of points:

a P(4,0)and Q( 0 ,¡3) b R(2,¡5)and S(¡ 1 ,¡3)

3 Find the coordinates of the midpoint of the line segment joining A(8,¡3)and B(2,1).

4 Find the gradients of the lines in the following graphs:

ab

5 The graph alongside shows the distance travelled by a

train over a 2 hour journey between two cities.

a Find the average speed from:

i OtoA ii AtoB iii BtoC

b Compare your answers toawith the gradients of the

line segments:

i OA ii AB iii BC

c Find the average speed for the whole journey.

6 Given A(2,¡1),B(¡ 5 ,3),C(3,4), classify triangle ABC as equilateral, isosceles or scalene.

7 Findkif the line joining X(2,¡3) and Y(¡ 1 ,k) is:

a parallel to a line with gradient^12

b perpendicular to a line with gradient¡^14.

8 Show that A(1,¡2),B(4,4)and C(5,6)are collinear.

x

y

A,(-10 ¡0) B,()10 ¡0

C,(6 )¡a

O

0

40

80

120

0123

time (h)

distance (km)

A

B

C

A

B

x

y

8

30

O

Consider the points A(¡ 3 ,7),B(1,8),C(4,0) and D(¡ 7 ,¡1). P, Q, R and S are the midpoints

of AB, BC, CD and DA respectively.

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Y:\HAESE\IGCSE01\IG01_12\272IGCSE01_12.CDR Tuesday, 18 November 2008 10:51:48 AM PETER