2.4: Perpendicular bisector of $AB$ is a given line

0606/21/M/J/19 — Question 10 · 8 marks

Solutions to this question by accurate drawing will not be accepted.

The points

A

and

B

have coordinates

(p, 3)

and

(1, 4)

respectively and the line

L

has equation

3x + y = 2

(i)

Given that the gradient of

AB

\dfrac{1}{3}

, find the value of

p

[2]

(ii)

Show that

L

is the perpendicular bisector of

AB

[3]

(iii)

Given that

C(q, -10)

lies on

L

, find the value of

q

[1]

(iv)

Find the area of triangle

ABC

[2]

2.4: Perpendicular bisector of ABABAB is a given line