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

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

$\left(\begin{array}{cc}\cos (\theta )& -\sin (\theta )\\ \sin (\theta )& \cos (\theta )\end{array}\right)$

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

$\left(\begin{array}{cc}\cos (90°)& -\sin (90°)\\ \sin (90°)& \cos (90°)\end{array}\right)$

Simplifying this matrix:

$\left(\begin{array}{cc}0& -1\\ 1& 0\end{array}\right)$

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

$\left(\begin{array}{cc}0& -1\\ 1& 0\end{array}\right)\left(\begin{array}{c}2\\ 4\end{array}\right)$

Performing the matrix multiplication:

$\left(\begin{array}{cc}0& -1\\ 1& 0\end{array}\right)\left(\begin{array}{c}2\\ 4\end{array}\right)=\left(\begin{array}{c}-4\\ 2\end{array}\right)$

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