Question

Given point A (2, 4) on the triangle is quadrant I how would you describe the coordinates of the new point when the triangle is rotated 90° counterclockwise

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the coordinates of the new point after rotating the triangle 90° counterclockwise, we can use the following rotation matrix:

\(\begin{pmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{pmatrix}\)

In this case, since we are rotating counterclockwise by 90°, we have:

\(\begin{pmatrix} \cos(90°) & -\sin(90°) \\ \sin(90°) & \cos(90°) \end{pmatrix}\)

Simplifying this matrix:

\(\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}\)

Now, we can apply this matrix transformation to the coordinates of point A (2, 4):

\(\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} 2 \\ 4 \end{pmatrix}\)

Performing the matrix multiplication:

\(\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} 2 \\ 4 \end{pmatrix} = \begin{pmatrix} -4 \\ 2 \end{pmatrix}\)

Thus, the coordinates of the new point after rotating the triangle 90° counterclockwise are (-4, 2).