Question

the graphs represent a rotation around a fixed point.
pre - image
image
which statement correctly describes the rotation from the pre - image to the image?
a. $90^{circ}$ clockwise rotation around the point $(2,2)$
b. $90^{circ}$ clockwise rotation around the point $(1,1)$
c. $180^{circ}$ clockwise rotation around the point $(2,2)$
d. $180^{circ}$ clockwise rotation around the point $(1,1)$

Explanation:

Step1: Identify pre-image vertices

Let's take 3 vertices of the pre-image rectangle: $(-3, 2)$, $(-3, 3)$, $(0, 2)$

Step2: Test option B (90° clockwise around (1,1))

First, use the 90° clockwise rotation rule around a point $(h,k)$:
For a point $(x,y)$, the rotated point is $(h + (y - k), k - (x - h))$

• For $(-3,2)$: $(1 + (2-1), 1 - (-3-1)) = (1+1, 1+4)=(2,5)$
• For $(-3,3)$: $(1 + (3-1), 1 - (-3-1))=(1+2,1+4)=(3,5)$
• For $(0,2)$: $(1 + (2-1), 1 - (0-1))=(1+1,1+1)=(2,2)$

These match the vertices of the image rectangle.

Step3: Verify other options (elimination)

• Option A: Rotating around (2,2) gives points that don't match the image.
• Option C/D: 180° rotation would map the pre-image to a position opposite the center, not the tall vertical rectangle seen.

Answer:

B. 90° clockwise rotation around the point (1,1)