Question

1. quadrilateral abcd and its image, abcd, are shown on the coordinate grid below. which rule best describes the transformation that was used to form quadrilateral abcd? a) (x,y)→(−y,x) b) (x,y)→(x,−y) c) (x,y)→(y,x) d) (x,y)→(−y,−x)

Explanation:

Step1: Recall rotation rules

A 90 - degree clock - wise rotation about the origin has the rule $(x,y)\to(y, - x)$, a 90 - degree counter - clockwise rotation about the origin has the rule $(x,y)\to(-y,x)$, a 180 - degree rotation about the origin has the rule $(x,y)\to(-x,-y)$.

Step2: Analyze the transformation

By observing the quadrilateral ABCD and its image A'B'C'D', we can see that it is a 90 - degree counter - clockwise rotation about the origin. For a point $(x,y)$ in ABCD, its corresponding point in A'B'C'D' follows the rule $(x,y)\to(-y,x)$.

Answer:

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