Let R(θ) denote a rotation matrix which rotates a point $x$ in $S^2$ anticlockwise about the origin through a given angle θ. (Where $S$ is the set of real numbers)
How do you illustrate that this preserves lines, distances and angles by rotating the triangle with vertices (1, 2),(2, 8),(3, 2) through an angle $π/2$?
The general form for a two dimensional rotation matrix is $\begin{bmatrix} \cos(\theta)&-\sin(\theta)\\ \sin(\theta)&\cos(\theta) \end{bmatrix}$
Plugging in your value of $\pi/2$, we get: $\begin{bmatrix} 0&-1\\ 1&0 \end{bmatrix}$
You should try and convince yourself this makes intuitive sense by applying it to $e_{1}$ and $e_{2}$ and seeing what it does (remember that a matrix or linear map is defined by what it does to basis vectors) or better yet, apply it to the three points that are the vertices of your triangle, and see what it does.