7 [Figure 1, printed on the insert, is provided for use in this question.]
The diagram shows a triangle with vertices \(A ( 1,1 ) , B ( 3,1 )\) and \(C ( 3,2 )\).
\includegraphics[max width=\textwidth, alt={}, center]{5bfb4d19-8772-43d7-b667-bd124d2504a8-04_1114_1141_552_360}
- The triangle \(D E F\) is obtained by applying to triangle \(A B C\) the transformation T represented by the matrix
$$\left[ \begin{array} { r r }
2 & 2
- 2 & 2
\end{array} \right]$$
- Calculate the coordinates of \(D , E\) and \(F\).
- Draw the triangle \(D E F\) on Figure 1.
- Given that T is a combination of an enlargement and a rotation, find the exact value of:
- the scale factor of the enlargement;
- the magnitude of the angle of the rotation.