Question

which shows the image of triangle wxy after the transformation $r_{0, - 90^{circ}}(x,y)$?

Explanation:

Step1: Recall rotation rule

The transformation $R_{0,- 90^{\circ}}(x,y)=(y, - x)$ represents a $90^{\circ}$ clock - wise rotation about the origin. For a point $(x,y)$ in the original triangle, its new coordinates after a $90^{\circ}$ clock - wise rotation about the origin will be $(y,-x)$.

Step2: Analyze the orientation change

When a shape is rotated $90^{\circ}$ clock - wise about the origin, the orientation of the shape changes. The vertical sides of the original triangle will become horizontal and the horizontal sides will become vertical in the rotated image. Also, the triangle will move to a new position in the coordinate plane according to the rotation rule for each of its vertices.

Answer:

(Without seeing the actual options clearly, it's not possible to provide a specific choice. But the correct image will have the triangle rotated 90 degrees clock - wise about the origin with vertices transformed as per the rule $(x,y)\to(y, - x)$)