AQA FP1 2013 June — Question 8

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2013
SessionJune
TopicLinear transformations

8 The diagram shows two triangles, \(T _ { 1 }\) and \(T _ { 2 }\).
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  1. Find the matrix which represents the stretch that maps triangle \(T _ { 1 }\) onto triangle \(T _ { 2 }\).
  2. The triangle \(T _ { 2 }\) is reflected in the line \(y = \sqrt { 3 } x\) to give a third triangle, \(T _ { 3 }\). Find, using surd forms where appropriate:
    1. the matrix which represents the reflection that maps triangle \(T _ { 2 }\) onto triangle \(T _ { 3 }\);
    2. the matrix which represents the combined transformation that maps triangle \(T _ { 1 }\) onto triangle \(T _ { 3 }\).
      (2 marks)