Edexcel FP1 2014 June — Question 7

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionJune
TopicLinear transformations

7. (i) In each of the following cases, find a \(2 \times 2\) matrix that represents
  1. a reflection in the line \(y = - x\),
  2. a rotation of \(135 ^ { \circ }\) anticlockwise about \(( 0,0 )\),
  3. a reflection in the line \(y = - x\) followed by a rotation of \(135 ^ { \circ }\) anticlockwise about \(( 0,0 )\).
    (ii) The triangle \(T\) has vertices at the points \(( 1 , k ) , ( 3,0 )\) and \(( 11,0 )\), where \(k\) is a constant. Triangle \(T\) is transformed onto the triangle \(T ^ { \prime }\) by the matrix $$\left( \begin{array} { r r } 6 & - 2
    1 & 2 \end{array} \right)$$ Given that the area of triangle \(T ^ { \prime }\) is 364 square units, find the value of \(k\).