Question

Given point A(2, 6) on the triangle, where would the new point on the triangle be after a rotation of 90 degrees counterclockwise?

(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To rotate a point counterclockwise by 90 degrees, we can apply the following rotation matrix:

\[\begin{bmatrix}
0 & -1 \\
1 & 0 \\
\end{bmatrix}\]

Let's apply this matrix to point A(2, 6):

\[\begin{bmatrix}
0 & -1 \\
1 & 0 \\
\end{bmatrix}
\begin{bmatrix}
2 \\
6 \\
\end{bmatrix}
=
\begin{bmatrix}
-6 \\
2 \\
\end{bmatrix}\]

Therefore, the new point after a rotation of 90 degrees counterclockwise is B(-6, 2).