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:

\(\begin{pmatrix}\cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta)\end{pmatrix}\)

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

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

\(\begin{pmatrix}\cos(\pi/2) & -\sin(\pi/2) \\ \sin(\pi/2) & \cos(\pi/2)\end{pmatrix} \begin{pmatrix}1 \\ 2\end{pmatrix} = \begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix} \begin{pmatrix}1 \\ 2\end{pmatrix} = \begin{pmatrix}0 \\ 1\end{pmatrix}\)

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