Augmented matrices for translations

A question is this type if and only if it uses 3×3 augmented matrices to represent transformations including translations in 2D, or asks about fixed points of such transformations.

3 questions · Standard +0.6

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WJEC Further Unit 1 2018 June Q8
9 marks Standard +0.8
8. The transformation \(T\) in the plane consists of a translation in which the point \(( x , y )\) is transformed to the point \(( x - 1 , y + 1 )\), followed by a reflection in the line \(y = x\).
  1. Determine the \(3 \times 3\) matrix which represents \(T\).
  2. Find the equation of the line of fixed points of \(T\).
  3. Find \(T ^ { 2 }\) and hence write down \(T ^ { - 1 }\).
WJEC Further Unit 1 2023 June Q4
7 marks Standard +0.3
4. The transformation \(T\) in the plane consists of a translation in which the point \(( x , y )\) is transformed to the point ( \(x + 2 , y - 2\) ), followed by a reflection in the line \(y = x\).
  1. Determine the \(3 \times 3\) matrix which represents \(T\).
  2. Determine how many invariant points exist under the transformation \(T\).
WJEC Further Unit 1 Specimen Q6
9 marks Standard +0.8
6. The transformation \(T\) in the plane consists of a reflection in the line \(y = x\), followed by a translation in which the point \(( x , y )\) is transformed to the point \(( x + 1 , y - 2 )\),followed by an anticlockwise rotation through \(90 ^ { \circ }\) about the origin.
  1. Find the \(3 \times 3\) matrix representing \(T\).
  2. Show that \(T\) has no fixed points.