Let and be fixed points in the plane.

MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

Let

A(2,-3)

and

B(10,5)

be fixed points in the plane. (i) Prove that the set of all points

P

for which

PA=PB

is the perpendicular bisector of

AB

, and find its Cartesian equation. (ii) If

P

is the point on this locus whose

x

-coordinate is

4

, determine the coordinates of

P

. (iii) Through

P

draw a line whose slope is

\dfrac{3}{2}

. A point

Q

lies on this line such that

PQ=6

units. Calculate the coordinates of all possible positions of

Q

, showing every step of your working.