Question

which coordinate represents the image’s center of rotation? (image shows a coordinate grid with a red preimage triangle and a dotted image triangle, with grid lines and axes labeled.)

Explanation:

Step1: Identify corresponding points

Preimage: (1,2), (1,4), (4,2); Image: (-1,0), (-1,-2), (-4,0)

Step2: Set up distance equations for center (h,k)

For (1,2) & (-1,0): (1-h)²+(2-k)²=(-1-h)²+(-k)² ⇒ h+k=1

Step3: Use second pair (1,4) & (-1,-2)

(1-h)²+(4-k)²=(-1-h)²+(-2-k)² ⇒ h+3k=3

Step4: Solve equations h+k=1 and h+3k=3

Subtract: 2k=2 ⇒ k=1, then h=0

Answer:

(0, 1)