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: Analyze rotation rule

The rule $R_{0,90^{\circ}}(x,y)$ rotates a point $(x,y)$ counter - clockwise about the origin by $90^{\circ}$. The transformation is $(x,y)\to(-y,x)$.

Step2: Analyze reflection rule

The rule $r_{y - axis}$ reflects a point across the y - axis. The transformation is $(x,y)\to(-x,y)$.

Step3: Apply transformations in order

First, apply the rotation $R_{0,90^{\circ}}$ to the vertices of $\triangle ABC$, then apply the reflection $r_{y - axis}$ to the result of the rotation. After performing these two transformations on the vertices of $\triangle ABC$, we can match the final image with the given triangles.

Answer:

4