Given point A (2,6) on the triangle, where would the new point on the triangle be after rotation of 90° clockwise?
To find the new point after a 90° clockwise rotation, we can use the rotation matrix:
\[
\begin{bmatrix}
\cos(-90°) & -\sin(-90°) \\
\sin(-90°) & \cos(-90°)
\end{bmatrix}
\begin{bmatrix}
x \\
y
\end{bmatrix}
\]
Since we are rotating the point A(2, 6), we can substitute its coordinates into the matrix formula:
\[
\begin{bmatrix}
\cos(-90°) & -\sin(-90°) \\
\sin(-90°) & \cos(-90°)
\end{bmatrix}
\begin{bmatrix}
2 \\
6
\end{bmatrix}
\]
Evaluating the matrix multiplication:
\[
\begin{bmatrix}
\cos(-90°) & -\sin(-90°) \\
\sin(-90°) & \cos(-90°)
\end{bmatrix}
\begin{bmatrix}
2 \\
6
\end{bmatrix}
= \begin{bmatrix}
0 & -1 \\
1 & 0
\end{bmatrix}
\begin{bmatrix}
2 \\
6
\end{bmatrix}
\]
\[
= \begin{bmatrix}
0(2) + (-1)(6) \\
1(2) + 0(6)
\end{bmatrix}
= \begin{bmatrix}
-6 \\
2
\end{bmatrix}
\]
Therefore, after a 90° clockwise rotation, the new point would be (-6, 2) on the triangle.