Question

a triangle is rotated 90° about the origin. which rule describes the transformation? (x,y)→(−x,−y) (x,y)→(−y,x) (x,y)→(−y,−x) (x,y)→(y,−x)

Explanation:

Step1: Recall rotation rule

When a point $(x,y)$ is rotated 90° counter - clockwise about the origin, the new coordinates $(x',y')$ are given by the transformation rule $(x,y)\to(-y,x)$.

Step2: Analyze options

We check each option against the correct 90 - degree rotation rule. The first option $(x,y)\to(-x,-y)$ is a 180 - degree rotation about the origin. The third option $(x,y)\to(-y,-x)$ is a 270 - degree counter - clockwise (or 90 - degree clockwise) rotation about the origin. The fourth option $(x,y)\to(y,-x)$ is not a standard rotation about the origin.

Answer:

$(x,y)\to(-y,x)$