point a is the original point before rotating which point represents a after a(4,1) is rotated 90° counterclockwise b, c d, e, f, g or h
To determine the point that represents A after a(4,1) is rotated 90° counterclockwise, we can apply the rotation matrix:
\[
\begin{bmatrix}
\cos(90^\circ) & -\sin(90^\circ) \\
\sin(90^\circ) & \cos(90^\circ) \\
\end{bmatrix}
\begin{bmatrix}
4 \\
1 \\
\end{bmatrix}
\]
Simplifying the matrix multiplication:
\[
\begin{bmatrix}
0 & -1 \\
1 & 0 \\
\end{bmatrix}
\begin{bmatrix}
4 \\
1 \\
\end{bmatrix}
=
\begin{bmatrix}
-1 \\
4 \\
\end{bmatrix}
\]
Therefore, the point that represents A after the rotation is (-1, 4).