Question

triangle xyz is rotated to create the image triangle xyz. which rules could describe the rotation? select two options. r0,90° r0,180° r0,270° (x,y)→(−y,x) (x,y)→(−x,−y)

Explanation:

Step1: Recall rotation rules

In a coordinate - plane, a rotation of $180^{\circ}$ about the origin $(0,0)$ has the rule $(x,y)\to(-x,-y)$. Also, the notation $R_{0,180^{\circ}}$ represents a rotation of $180^{\circ}$ about the origin.

Step2: Analyze the triangle's rotation

By observing the pre - image $\triangle XYZ$ and the image $\triangle X'Y'Z'$, we can see that the triangle is rotated $180^{\circ}$ about the origin.

Answer:

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