Question

10.4.2 quiz: transformations
a. rotate 180 degrees counterclockwise about the origin, then translate 2 units down.
b. rotate 90 degrees counterclockwise about the origin, then translate 2 units up.
c. rotate 90 degrees counterclockwise about the origin, then translate 2 units down.
d. rotate 180 degrees counterclockwise about the origin, then translate 2 units up.

Explanation:

Step1: Analyze rotation

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(-y,x)\).

Step2: Analyze translation

After rotation, translating 2 units down means subtracting 2 from the \(y\) - coordinate of the rotated point. The combined transformation (rotation followed by translation) matches the transformation from the original rectangle (with vertices \(A,B,C,D\)) to the new rectangle (with vertices \(A',B',C',D'\)) as shown in the graph.

Answer:

C. Rotate 90 degrees counterclockwise about the origin, then translate 2 units down.