3. 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.
  1. 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 .
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