CAIE P1 2019 June — Question 4

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionJune
TopicStraight Lines & Coordinate Geometry

4
\includegraphics[max width=\textwidth, alt={}, center]{ebf16cae-1e80-44d2-9c51-630f5dc3c11f-06_625_750_260_699} The diagram shows a trapezium \(A B C D\) in which the coordinates of \(A , B\) and \(C\) are (4, 0), (0, 2) and \(( h , 3 h )\) respectively. The lines \(B C\) and \(A D\) are parallel, angle \(A B C = 90 ^ { \circ }\) and \(C D\) is parallel to the \(x\)-axis.
  1. Find, by calculation, the value of \(h\).
  2. Hence find the coordinates of \(D\).