8 The \(2 \times 2\) matrix A represents a transformation T which has the following properties.
- The image of the point \(( 0,1 )\) is the point \(( 3,4 )\).
- An object shape whose area is 7 is transformed to an image shape whose area is 35 .
- T has a line of invariant points.
- Find a possible matrix for \(\mathbf { A }\).
The transformation S is represented by the matrix \(\mathbf { B }\) where \(\mathbf { B } = \left( \begin{array} { l l } 3 & 1
2 & 2 \end{array} \right)\).
Find the equation of the line of invariant points of S .Show that any line of the form \(y = x + c\) is an invariant line of S .