2.12: Perpendicular line through midpoint; distance PMPM

0606/22/O/N/19 — Question 9 · 11 marks

2.12 diagram
The diagram shows the points A(3,5)A(-3, 5) and B(5,1)B(5, -1). The mid-point of ABAB is MM and the line PMPM is perpendicular to ABAB. The point PP has coordinates (r,s)(r, s).
(i)
Find the equation of the line PMPM in the form y=mx+cy = mx + c, where mm and cc are exact constants.
[5]
(ii)
Hence find an expression for ss in terms of rr.
[1]
(iii)
Given that the length of PMPM is 10 units, find the value of rr and of ss.
[5]