1. Draw the image of the figure under the given rotation. Make sure to label appropriately. Quadrilateral PQRS; $270^{\circ}$ about the origin. Transformation Rule: $(x, y) \rightarrow$ \begin{tabular}{l|l|l|} \cline { 2 - 3 } & \multicolumn{1}{|c|}{ Preimage Coordinates } & Image \\ \hline & $(x, y)$ & \\ $Q$ & $(-1,-2)$ & \\ $R$ & $(1,-3)$ & \\ $S$ & $(-3,-4)$ & \\ \hline$P$ & $(-4,-3)$ & \\ \hline \end{tabular}
Solution
Step 1 ：Given a quadrilateral PQRS with coordinates Q(-1, -2), R(1, -3), S(-3, -4), P(-4, -3).
Step 2 ：We are asked to perform a rotation transformation of $270^{\circ}$ about the origin on this quadrilateral.
Step 3 ：The general rule for a rotation of $270^{\circ}$ about the origin is \((x, y) \rightarrow (y, -x)\). This means that for each point, the new x-coordinate will be the old y-coordinate and the new y-coordinate will be the negative of the old x-coordinate.
Step 4 ：Applying this rule to each point of the quadrilateral, we get the new coordinates as follows: Q'(-2, 1), R'(-3, -1), S'(-4, 3), P'(-3, 4).
Step 5 ：\(\boxed{\text{The image of the quadrilateral PQRS after a } 270^{\circ} \text{ rotation about the origin has the following coordinates: Q'(-2, 1), R'(-3, -1), S'(-4, 3), P'(-3, 4).}}\)
