Answer to Question #184793 in Geometry for gabby

Question

a dilation with center c and a scale factor k maps A onto D and B onto E . If AB = 4 and DE =10 , find k

Answer 1

Let (x,y) be a vertex of the figure.

Translate so the origin becomes center of the dilation (left 4 and up 2): (x - 4, y + 2).

Apply the dilation formula when centered at origin: (3(x - 4), 3(y + 2)) = (3x - 12, 3y + 6)

Translate back (right 4 and down 2): (3x - 12 + 4, 3y + 6 - 2) = (3x - 8, 3y + 4)

Rule: (x,y) → (3x - 8, 3y + 4)

For example, under this dilation, the point (5,6) becomes (3(5)-8, 3(6)+4) which is (7,22).