CAIE P1 2012 November — Question 5

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionNovember
TopicStraight Lines & Coordinate Geometry

5
\includegraphics[max width=\textwidth, alt={}, center]{11bfe5bd-604c-43e5-81e7-4c1f5676bcbb-3_602_751_255_696} The diagram shows a triangle \(A B C\) in which \(A\) has coordinates ( 1,3 ), \(B\) has coordinates ( 5,11 ) and angle \(A B C\) is \(90 ^ { \circ }\). The point \(X ( 4,4 )\) lies on \(A C\). Find
  1. the equation of \(B C\),
  2. the coordinates of \(C\).