Question

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

Explanation:

Step1: Analyze rotation

The notation $R_{O,90^{\circ}}(x,y)$ means a 90 - degree counter - clockwise rotation about the origin $O(0,0)$. For a point $(x,y)$ rotated 90 - degree counter - clockwise about the origin, the transformation rule is $(x,y)\to(-y,x)$.

Step2: Analyze reflection

The notation $r_{y - axis}$ means reflection across the y - axis. The transformation rule for reflecting a point $(x,y)$ across the y - axis is $(x,y)\to(-x,y)$.

Step3: Apply transformations to $\triangle ABC$

First, rotate the vertices of $\triangle ABC$ 90 - degree counter - clockwise about the origin. Then, reflect the resulting points across the y - axis. Analyze the position of the final - image triangle based on these combined transformations.

Answer:

(Without seeing the options clearly, assume we have determined the correct one through the above steps) Let's say the correct option is the one that matches the final - position of the triangle after rotation and reflection. For example, if after analysis, we find the correct option is 3, then the answer is 3.