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

4.03d Linear transformations 2D: reflection, rotation, enlargement, shear
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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 2018 June Q8
9 marks Standard +0.8
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 \(T\). [4]
  2. Find the equation of the line of fixed points of \(T\). [2]
  3. Find \(T^2\) and hence write down \(T^{-1}\). [3]
WJEC Further Unit 1 Specimen Q6
9 marks Standard +0.8
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 \(90°\) about the origin.
  1. Find the \(3 \times 3\) matrix representing \(T\). [6]
  2. Show that \(T\) has no fixed points. [3]