1.1: Perpendicular from a point to a line

0606/11/M/J/16 — Question 8 · 10 marks

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

Three points have coordinates A(−8,6)A(-8, 6), B(4,2)B(4, 2) and C(−1,7)C(-1, 7). The line through CC perpendicular to ABAB intersects ABAB at the point PP.
(i)
Find the equation of the line ABAB.
[2]
(ii)
Find the equation of the line CPCP.
[2]
(iii)
Show that PP is the midpoint of ABAB.
[3]
(iv)
Calculate the length of CPCP.
[1]
(v)
Hence find the area of the triangle ABCABC.
[2]