Giving a point one, two on a geometric figure what is the new point when the figure is rotated counterclockwise 90 degrees

Answer 1

To determine the new coordinates of a point when a geometric figure is rotated counterclockwise by 90 degrees, we will use the following rotation matrix:

$\left(\begin{array}{cc}\cos (\theta )& -\sin (\theta )\\ \sin (\theta )& \cos (\theta )\end{array}\right)$

where $\theta ={90}^{\circ }$ (converted to radians: $\pi /2$).

Using the given point (x, y) = (1, 2):

$\left(\begin{array}{cc}\cos (\pi /2)& -\sin (\pi /2)\\ \sin (\pi /2)& \cos (\pi /2)\end{array}\right)\left(\begin{array}{c}1\\ 2\end{array}\right)=\left(\begin{array}{cc}0& -1\\ 1& 0\end{array}\right)\left(\begin{array}{c}1\\ 2\end{array}\right)=\left(\begin{array}{c}0\\ 1\end{array}\right)$

Therefore, after rotating counterclockwise by 90 degrees, the new point becomes (0, 1).