Cambridge International Mathematics

Coordinate geometry (Chapter 12) 269

)

¡ 4

a¡ 2

=

¡ 2

1

μ

a¡ 2

a¡ 2

¶

fachieving a common denominatorg

) ¡4=¡2(a¡2) fequating numeratorsg

) ¡4=¡ 2 a+4

) 2 a=8

) a=4

Example 16 Self Tutor

Findtgiven that the line joining D(¡ 1 ,¡3) to C(1,t) is

perpendicular to a line with gradient 2.

gradient of DC =¡^12 fperpendicular to line of gradient 2 g

)

t¡¡ 3

1 ¡¡ 1

=¡^12

)

t+3

2

=

¡ 1

2

fsimplifyingg

) t+3=¡ 1 fequating numeratorsg

) t=¡ 4

EXERCISE 12E.1

1 Find the gradient of all lines perpendicular to a line with a gradient of:

a^12 b^25 c 3 d 7 e ¡^25 f ¡ 213 g ¡ 5 h ¡ 1

2 The gradients of two lines are listed below. Which of the line pairs are perpendicular?

a^13 , 3 b 5 ,¡ 5 c^37 ,¡ 213 d 4 ,¡^14

e 6 ,¡^56 f^23 ,¡^32 g

p

q

,

q

p

h

a

b

,¡

b

a

3 Findagiven that the line joining:

a A(1,3) to B(3,a) is parallel to a line with gradient 3

b P(a,¡3) to Q(4,¡2) is parallel to a line with gradient^13

c M(3,a) to N(a,5) is parallel to a line with gradient¡^25.

4 Findtgiven that the line joining:

a A(2,¡3) to B(¡ 2 ,t) is perpendicular to a line with gradient (^114)
b C(t,¡2) to D(1,4) is perpendicular to a line with gradient^23
c P(t,¡2) to Q(5,t) is perpendicular to a line with gradient¡^14.
5 Given the points A(1,4),B(¡ 1 ,0),C(6,3) and D(t,¡1), findtif:
a AB is parallel to CD b AC is parallel to DB
c AB is perpendicular to CD d AD is perpendicular to BC.
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y:\HAESE\IGCSE01\IG01_12\269IGCSE01_12.CDR Thursday, 25 September 2008 12:13:42 PM PETER