Edexcel P1 2020 January — Question 6

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2020
SessionJanuary
TopicStraight Lines & Coordinate Geometry

6. The line \(l _ { 1 }\) has equation \(3 x - 4 y + 20 = 0\) The line \(l _ { 2 }\) cuts the \(x\)-axis at \(R ( 8,0 )\) and is parallel to \(l _ { 1 }\)
  1. Find the equation of \(l _ { 2 }\), writing your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers to be found. The line \(l _ { 1 }\) cuts the \(x\)-axis at \(P\) and the \(y\)-axis at \(Q\).
    Given that \(P Q R S\) is a parallelogram, find
  2. the area of \(P Q R S\),
  3. the coordinates of \(S\).