Question

rotating a negative number of degrees
which shows the image of triangle wxy after the transformation ( r_{0,-90^{circ}}(x, y) )?

Explanation:

Step1: Recall the rotation rule

The rule for a rotation of \(R_{O,-90^{\circ}}(x,y)\) (a \(90^{\circ}\) clockwise rotation about the origin) is \((x,y)\to(y, -x)\).

Step2: Analyze the position of each vertex

Let's assume the original vertices of \(\triangle WXY\). After applying the rotation rule \((x,y)\to(y, -x)\), we can check the orientation and position of the new triangle. A \( - 90^{\circ}\) rotation (clockwise) will change the position of the triangle such that it is rotated \(90^{\circ}\) clockwise from its original position.

Answer:

The second option (the one with \(Y'\) in the second - quadrant, \(W'\) and \(X'\) in a position corresponding to a \(90^{\circ}\) clockwise rotation) is the correct image of \(\triangle WXY\) after the transformation \(R_{O,-90^{\circ}}(x,y)\).