Question

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

Explanation:

Step1: Recall rotation rules

A 180 - degree rotation about the origin has the rule \((x,y)\to(-x,-y)\).

Step2: Check the transformation

By observing the original parallelogram \(ABCD\) and its image \(A'B'C'D'\), we can see that each point \((x,y)\) of the original figure is transformed to \((-x,-y)\) in the new figure. For example, if we take a vertex of the parallelogram with coordinates \((x,y)\), its corresponding vertex in the rotated parallelogram has coordinates \((-x,-y)\).

Answer:

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