The center of dilation is (1, -1)
The scale factor is 1/3
Image showing the dilation is attached
How to find the center of dilation
The scale factor is solved using some sides as reference. Let us use CA to C'A
preimage dimension * scale facto, k = image dimension
CA * k = C'A'
9 * k = 3
k = 3/9 = 1/3
Solving for center of dilation. (x₀, y₀)
x₀ = (k(x₁) - x₂) / (k - 1) and y₀ = (k(y₁) - y₂) / (k - 1)
Using points C (-2, 5) and C' (0, 1)
x₀ = (1/3(-2) - 0) / (1/3 - 1)
x₀ = -2/3 / -2/3
x₀ = 1
y₀ = (1/3(5) - 1) / (1/3 - 1)
y₀ = (5/3 - 1) / (-2/3)
y₀ = (2/3) / (-2/3)
y₀ = -1
the center of dilation is (1, -1)