square pqrs is transformed as shown on the graph. which rule describes the transformation? o…

square pqrs is transformed as shown on the graph. which rule describes the transformation? o $r_{0,90^{circ}}$ o $r_{0,180^{circ}}$ o $r_{0,270^{circ}}$ o $r_{0,360^{circ}}$

square pqrs is transformed as shown on the graph. which rule describes the transformation? o $r_{0,90^{circ}}$ o $r_{0,180^{circ}}$ o $r_{0,270^{circ}}$ o $r_{0,360^{circ}}$

Answer

Explanation:

Step1: Recall rotation rules

A rotation of $R_{0,90^{\circ}}$ about the origin $(0,0)$ transforms a point $(x,y)$ to $(-y,x)$. A rotation of $R_{0,180^{\circ}}$ transforms $(x,y)$ to $(-x,-y)$. A rotation of $R_{0,270^{\circ}}$ transforms $(x,y)$ to $(y, - x)$. A rotation of $R_{0,360^{\circ}}$ transforms $(x,y)$ to $(x,y)$.

Step2: Analyze the graph

By observing the positions of the vertices of square $PQRS$ and its image $P'Q'R'S'$, we can see that the square is rotated 180 - degrees about the origin. For example, if we consider a vertex of the original square at a positive - x and positive - y position, its corresponding vertex in the image is at the negative - x and negative - y position.

Answer:

$R_{0,180^{\circ}}$