CAIE P1 2018 June — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2018
SessionJune
TopicStraight Lines & Coordinate Geometry

6 The coordinates of points \(A\) and \(B\) are \(( - 3 k - 1 , k + 3 )\) and \(( k + 3,3 k + 5 )\) respectively, where \(k\) is a constant ( \(k \neq - 1\) ).
  1. Find and simplify the gradient of \(A B\), showing that it is independent of \(k\).
  2. Find and simplify the equation of the perpendicular bisector of \(A B\).