Parallelogram $Q R S T$ has vertices $Q(-4,2), R(-2,4), S(0,1)$, and $T(-2,1)$. Draw and label the image after a counterclockwise rotation of $270^{\circ}$ about the origin. (1 point) Transformation Rule: \begin{tabular}{|c|c|} \hline $\begin{array}{c}\text { Preimage Coordinates } \\ (x, y)\end{array}$ & Image \\ \hline & \\ \hline & \\ \hline & \\ \hline & \\ \hline \end{tabular}
Solution
Step 1 ：The problem provides the vertices of a parallelogram $Q R S T$ as $Q(-4,2), R(-2,4), S(0,1)$, and $T(-2,1)$.
Step 2 ：We are asked to find the new coordinates of the vertices after a counterclockwise rotation of $270^{\circ}$ about the origin.
Step 3 ：The transformation rule for a counterclockwise rotation of $270^{\circ}$ about the origin is $(x, y) \rightarrow (y, -x)$. This means that the x-coordinate of each point becomes the y-coordinate of the new point, and the y-coordinate of each point becomes the negative of the x-coordinate of the new point.
Step 4 ：Applying this rule to the given vertices, we get the new vertices as $(2, 4), (4, 2), (1, 0), (1, 2)$.
Step 5 ：Thus, the new coordinates of the vertices of the parallelogram after a counterclockwise rotation of $270^{\circ}$ about the origin are \(\boxed{(2, 4), (4, 2), (1, 0), (1, 2)}\).
