Cambridge International AS and A Level Mathematics Pure Mathematics 1

Co-ordinate geometry

P1^

2

The gradient of the line PQ is

35

24

2

6

1

3

–

–(–)

= =– –

and so the gradient of the perpendicular bisector is +3.

The perpendicular bisector passes throught the mid-point, R, of the line PQ. The

co-ordinates of R are

24

2

35

2

( +(–),(+ )i.e.–,^14 ).

Using y − y 1 = m(x − x 1 ), the equation of the perpendicular bisector is

y − 4 = 3(x − (−1))

y − 4 = 3 x + 3

y = 3 x + 7.

EXERCISE 2C 1 Find the equations of the lines (i) − (x) in the diagrams below.

–4 –2 0 2 4 6 8

–2

–4

2

4

6

x

y

–2 2 4 6 8

–2

2

6

x

y

(iii)

(ii)

(i)

(v)

(iv)

(vii)

(vi)

(x)

(viii)

(ix)

–4

–4 0

4