Question

triangle xyz is rotated to create the image triangle xyz. which rules could describe the rotation? select two options. $r_{0,90^{circ}}$ $r_{0,180^{circ}}$ $r_{0,270^{circ}}$ $(x,y)\to(-y,x)$ $(x,y)\to(-x,-y)$

Explanation:

Step1: Recall rotation rules

For a rotation of $180^{\circ}$ about the origin $(0,0)$, the rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$. The notation $R_{0,180^{\circ}}$ means a rotation of $180^{\circ}$ about the origin.

Step2: Analyze the graph

By observing the original triangle $XYZ$ and its image $X'Y'Z'$, we can see that each point $(x,y)$ of $\triangle XYZ$ has been transformed to $(-x,-y)$ in $\triangle X'Y'Z'$. This indicates a $180 - degree$ rotation about the origin. A $90 - degree$ rotation has the rule $(x,y)\to(-y,x)$ and a $270 - degree$ rotation has the rule $(x,y)\to(y, - x)$. So the rules that describe the rotation are $R_{0,180^{\circ}}$ and $(x,y)\to(-x,-y)$.

Answer:

B. $R_{0,180^{\circ}}$, E. $(x,y)\to(-x,-y)$