demonstrating the properties of rotations, if a line segment with endpoints (0-3) and 0,-7) is rotated 90 degrees clockwise, what is an endpoint of this rotated segment?
To rotate a point 90 degrees clockwise, we can use the following rotation matrix:
\[
\begin{bmatrix}
0 & -1\\
1 & 0
\end{bmatrix}
\]
Applying this matrix to the point (0,-3), we get:
\[
\begin{bmatrix}
0 & -1\\
1 & 0
\end{bmatrix}
\begin{bmatrix}
0\\
-3
\end{bmatrix}
=
\begin{bmatrix}
-3\\
0
\end{bmatrix}
\]
Therefore, the point (-3,0) is an endpoint of the rotated segment after rotating the original segment 90 degrees clockwise.