Question

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 \(R_{O,- 90^{\circ}}(x,y)\) is \((x,y)\to(y,-x)\)

Step2: Analyze the coordinates

Let's assume original coordinates of \(W\), \(X\), \(Y\). After applying the rotation \((x,y)\to(y,-x)\), the new coordinates (image points) will be in the second quadrant for non - origin points. The second option correctly positions the image of the triangle \(WXY\) according to the \((x,y)\to(y, - x)\) rotation rule.

Answer:

The second option (the one with \(W'\), \(X'\), \(Y'\) in the second quadrant)