Question

the rule $r_{y - axis} \circ r_{0,90\circ}(x,y)$ is applied to $\triangle abc$. which triangle shows the final image? o 1 o 2 o 3 o 4

Explanation:

Step1: Recall rotation rule

The rule $R_{0,90^{\circ}}(x,y)=(-y,x)$. Rotate $\triangle ABC$ 90 - degrees counter - clockwise about the origin.

Step2: Recall reflection rule

The rule $r_{y - axis}(x,y)=(-x,y)$. Reflect the rotated triangle across the y - axis.

Step3: Analyze the combined transformation

Applying the rotation first and then the reflection, we can check the position of the vertices of $\triangle ABC$ after both transformations. After rotating $\triangle ABC$ 90 - degrees counter - clockwise about the origin and then reflecting it across the y - axis, we find the final image.

Answer:

4