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.
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\caption{Fig. 9}
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- Write down the image of the point ( \(- 3,7\) ) under transformation T .
- Write down the image of the point \(( x , y )\) under transformation T .
- Find the \(2 \times 2\) matrix which represents the transformation.
- Describe the transformation M represented by the matrix \(\left( \begin{array} { r r } 0 & - 1
1 & 0 \end{array} \right)\). - Find the matrix representing the composite transformation of T followed by M .
- 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.