Let (x, y) be the centroid of a domain D. For > 0, let D be

Let (x̅, y̅) be the centroid of a domain D. For λ > 0, let λD be the dilation of D, defined by

λD = {(λx, λy) : (x, y) ∈ D}
Use the Change of Variables Formula to prove that the centroid of λD is (λx̅, λy̅).