Write down transformation matrix

A question is this type if and only if it asks to write down or state the matrix representing a specified transformation (e.g. rotation through given angle, reflection in given line, stretch with given parameters).

5 questions · Moderate -1.0

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Edexcel F1 2018 June Q2
7 marks Moderate -0.8
  1. The transformation represented by the \(2 \times 2\) matrix \(\mathbf { P }\) is an anticlockwise rotation about the origin through 45 degrees.
    1. Write down the matrix \(\mathbf { P }\), giving the exact numerical value of each element.
    $$\mathbf { Q } = \left( \begin{array} { c c } k \sqrt { 2 } & 0 \\ 0 & k \sqrt { 2 } \end{array} \right) \text {, where } k \text { is a constant and } k > 0$$
  2. Describe fully the single geometrical transformation represented by the matrix \(\mathbf { Q }\). The combined transformation represented by the matrix \(\mathbf { P Q }\) transforms the rhombus \(R _ { 1 }\) onto the rhombus \(R _ { 2 }\). The area of the rhombus \(R _ { 1 }\) is 6 and the area of the rhombus \(R _ { 2 }\) is 147
  3. Find the value of the constant \(k\).
OCR FP1 2008 January Q1
4 marks Easy -1.2
1 The transformation S is a shear with the \(y\)-axis invariant (i.e. a shear parallel to the \(y\)-axis). It is given that the image of the point \(( 1,1 )\) is the point \(( 1,0 )\).
  1. Draw a diagram showing the image of the unit square under the transformation S .
  2. Write down the matrix that represents S .
OCR FP1 2006 June Q2
4 marks Easy -1.2
2 The transformation S is a shear parallel to the \(x\)-axis in which the image of the point ( 1,1 ) is the point \(( 0,1 )\).
  1. Draw a diagram showing the image of the unit square under S .
  2. Write down the matrix that represents S .
OCR MEI FP1 2008 January Q9
13 marks Moderate -0.8
9 A transformation T acts on all points in the plane. The image of a general point P is denoted by \(\mathrm { P } ^ { \prime }\). \(\mathrm { P } ^ { \prime }\) always lies on the line \(y = x\) and has the same \(x\)-coordinate as P. This is illustrated in Fig. 9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{225bff01-f2c4-421f-ac91-c6a0fcb01e6f-4_807_825_402_660} \captionsetup{labelformat=empty} \caption{Fig. 9}
\end{figure}
  1. Write down the image of the point ( \(- 3,7\) ) under transformation T .
  2. Write down the image of the point \(( x , y )\) under transformation T .
  3. Find the \(2 \times 2\) matrix which represents the transformation.
  4. Describe the transformation M represented by the matrix \(\left( \begin{array} { r r } 0 & - 1 \\ 1 & 0 \end{array} \right)\).
  5. Find the matrix representing the composite transformation of T followed by M .
  6. Find the image of the point \(( x , y )\) under this composite transformation. State the equation of the line on which all of these images lie.
OCR Further Pure Core 2 2021 June Q1
8 marks Moderate -0.8
1 In this question you must show detailed reasoning.
S is the 2-D transformation which is a stretch of scale factor 3 parallel to the \(x\)-axis. A is the matrix which represents S .
  1. Write down \(\mathbf { A }\).
  2. By considering the transformation represented by \(\mathbf { A } ^ { - 1 }\), determine the matrix \(\mathbf { A } ^ { - 1 }\). Matrix \(\mathbf { B }\) is given by \(\mathbf { B } = \left( \begin{array} { c c } 0 & - 1 \\ - 1 & 0 \end{array} \right)\). T is the transformation represented by \(\mathbf { B }\).
  3. Describe T.
  4. Determine the matrix which represents the transformation S followed by T .
  5. Demonstrate, by direct calculation, that \(( \mathbf { B A } ) ^ { - 1 } = \mathbf { A } ^ { - 1 } \mathbf { B } ^ { - 1 }\).