- A point \(P\) is reflected in the line \(y = k x\), where \(k\) is a constant. It is then rotated anticlockwise about \(O\) through an acute angle \(\theta\), where \(\cos \theta = 0 \cdot 8\). The resulting transformation matrix is given by \(T\), where
$$T = \frac { 1 } { 85 } \left[ \begin{array} { r r }
- 84 & - 13
- 13 & 84
\end{array} \right]$$
- Determine the value of \(k\).
Find the invariant points of \(T\).