Question

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

Explanation:

Step1: Analyze the transformation rule

The rule $r_{y - axis}\circ R_{0, 90^{\circ}}(x,y)$ means first rotate the triangle $\triangle ABC$ counter - clockwise about the origin by $90^{\circ}$ and then reflect it over the $y$ - axis.

Step2: Apply rotation

When we rotate a point $(x,y)$ counter - clockwise about the origin by $90^{\circ}$, the transformation is $(x,y)\to(-y,x)$.

Step3: Apply reflection

After rotation, when we reflect a point $(x,y)$ over the $y$ - axis, the transformation is $(x,y)\to(-x,y)$.

Step4: Check the options

By applying these two transformations to the vertices of $\triangle ABC$ and comparing with the given options, we can determine the final image.

Answer:

(Without seeing the actual transformation results of the options, we can't give a specific option number. But the above steps show how to solve the problem. If you provide more details about the options' characteristics after transformation, we can give a definite answer.)