Question

triangle abc is rotated to create the image abc. which rule describes the transformation? (x, y)→(x, -y) (x, y)→(y, x) (x, y)→(-x, -y) (x, y)→(-y, -x)

Explanation:

Step1: Recall rotation rules

A rotation of 180 - degrees about the origin changes the sign of both the x - coordinate and the y - coordinate of a point \((x,y)\).

Step2: Analyze the transformation

When we compare the coordinates of the points of \(\triangle ABC\) and \(\triangle A'B'C'\), we can see that the transformation is a 180 - degree rotation about the origin. For a point \((x,y)\) in \(\triangle ABC\), its corresponding point in \(\triangle A'B'C'\) has coordinates \((-x,-y)\).

Answer:

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