Given a point (−5, 4) on a geometric figure, what is the new point after rotating the figure 90 degrees counterclockwise?
To rotate a point 90 degrees counterclockwise, we can use the following transformation matrix:
\[
\begin{bmatrix}
0 & -1 \\
1 & 0 \\
\end{bmatrix}
\]
Applying the matrix transformation to the point (-5, 4):
\[
\begin{bmatrix}
0 & -1 \\
1 & 0 \\
\end{bmatrix} \begin{bmatrix}
-5 \\
4 \\
\end{bmatrix} = \begin{bmatrix}
-4 \\
-5 \\
\end{bmatrix}
\]
So, the new point after rotating the figure 90 degrees counterclockwise is (-4, -5).