Question

question 3 of 10
what transformations were applied to abcd to obtain abcd?
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 down.
c. rotate 90 degrees counterclockwise about the origin, then translate 2 units up.
d. rotate 180 degrees counterclockwise about the origin, then translate 2 units up.

Explanation:

Step1: Analyze rotation

If we rotate a point $(x,y)$ 90 - degrees counter - clockwise about the origin, the new coordinates become $(-y,x)$. If we rotate a point $(x,y)$ 180 - degrees counter - clockwise about the origin, the new coordinates become $(-x,-y)$. Looking at the orientation of the rectangle $ABCD$ and $A'B'C'D'$, we can see that a 90 - degrees counter - clockwise rotation about the origin is applied first.

Step2: Analyze translation

After the rotation, we observe the vertical movement. The original rectangle is moved down by 2 units.

Answer:

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