PLEASE HELP THIS IS DUE SOON AND I WAS SICK SO I NEED HELP. The preimage ∆ABC has points at A(2,-2), B(5,-4), and C(1,-6) and is dilated by a certain scale factor from a certain center of dilation. The image of ∆A'B'C' has points at A'(-6,8), B'(3,2), and C'(-9,-4). Use only algebraic reasoning (NO GRAPHING) to find the coordinates of the center of dilation. Show all work used below and provide a complete written justification for your answer. Explain what you did and why you did it.

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18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²