Question

given rectangles abcd and abcd, describe the transformation that takes place from abcd to abcd. a reflection over the y - axis, then a reflection over the x - axis, and a 90° rotation clockwise about the origin a reflection over the x - axis, then a reflection over the y - axis, and a 90° rotation clockwise about the origin a 90° clockwise rotation about the origin and a translation of 7 units down a 90° counterclockwise rotation about the origin and a translation of 6 units to the right

Explanation:

Step1: Analyze rotation

A 90 - degree clockwise rotation about the origin $(x,y)\to(y, - x)$. For example, if $A=(-6,5)$ in rectangle $ABCD$, after a 90 - degree clockwise rotation about the origin, it would be $(5,6)$.

Step2: Analyze translation

A translation of 7 units down means subtracting 7 from the y - coordinate of each point. After rotation, if a point is $(x,y)$, after translation 7 units down, it becomes $(x,y - 7)$. This sequence of transformations matches the movement from rectangle $ABCD$ to $A'B'C'D'$.

Answer:

C. a 90° clockwise rotation about the origin and a translation of 7 units down