Cambridge International Mathematics

258 Coordinate geometry (Chapter 12)

2 On the same set of axes plot the following points:

a P(2,1) b Q(2,¡3) c R(¡ 3 ,¡1) d S(¡ 2 ,3)

e T(¡ 4 ,0) f U(0,¡1) g V(¡ 5 ,¡3) h W(4,¡2)

3 State the quadrant in which each of the points in question 2 lies.

4 On different sets of axes show all points with:

a x-coordinate equal to¡ 2 b y-coordinate equal to¡ 3

c x-coordinate equal to 0 d y-coordinate equal to 0

e negativex-coordinate f positivey-coordinate

g negativexandy-coordinates h positivexand negativey-coordinates

5 On separate axes plot the following sets of points:

a f(0,0),(1,¡1),(2,¡2),(3,¡3),(4,¡4)g

b f(¡ 2 ,3),(¡ 1 ,1),(0,¡1),(1,¡3),(2,¡5)g

i Are the points collinear?

ii Do any of the following rules fit the set of points?

A y=2x+1 B y=2x¡ 1 C y=x

D y=¡ 2 x¡ 1 E x+y=0

Consider the points A(1,3)and B(4,1):We can join the

points by a straight line segment of lengthdunits. Suppose

we draw a right angled triangle with hypotenuse AB and

with sides parallel to the axes.

It is clear that d^2 =3^2 +2^2 fPythagorasg

) d^2 =13

) d=

p

13 fas d> 0 g

) the distance from A to B is

p

13 units.

Example 3 Self Tutor

Find the distance between P(¡ 2 ,1) and Q(3,3):

We construct a right angled triangle with

shorter sides on the grid lines.

PQ^2 =5^2 +2^2 fPythagorasg

) PQ=29

) PQ=

p

29 units fPQ> 0 g

B DISTANCE BETWEEN TWO POINTS [7.1, 7.2]

With practice you

will not need to

use grid paper. A

neat sketch will do.

y

(^3) x
2
B (4, 1)
A (1, 3)
d
O
y
x
O
5
2
P
Q
-2 3
3
IGCSE01
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_12\258IGCSE01_12.CDR Thursday, 2 October 2008 12:37:22 PM PETER