Given the point (3,4) 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 rotation matrix:
\[
\begin{bmatrix}
0 & -1 \\
1 & 0 \\
\end{bmatrix}
\]
Applying this matrix to the given point (3,4), we get:
\[
\begin{bmatrix}
0 & -1 \\
1 & 0 \\
\end{bmatrix}
\begin{bmatrix}
3 \\
4 \\
\end{bmatrix}
= \begin{bmatrix}
-4 \\
3 \\
\end{bmatrix}
\]
Therefore, the new point after rotating the figure 90 degrees counterclockwise is (-4, 3).