Question

Triangles ABC has vertices A(1,-1) B(1,-5) and C(5,-5). A dilation with a scale factor of 0.25 and true center at (-3,3) is applied to the triangle. What are the coordinates of A’B’C’ in the dilated image?

Answer 1

• A'(-2, 2)
• B'(-2, 1)
• C'(-1, 1)

Explanation:

For scale factor k and center of dilation (p, q), the transformation is ...

(x, y) ⇒ (kx +(1-k)p, ky +(1-k)q)

For k=1/4 and (p, q) = (-3, 3), the coordinates are transformed to ...

(x, y) ⇒ (1/4x -9/4, 1/4y +9/4)

Then the preimage points are dilated to ...

A(1, -1) ⇒ A'(1/4 -9/4, -1/4 +9/4) = A'(-2, 2)

B(1, -5) ⇒ B'(1/4 -9/4, -5/4 +9/4) = B'(-2, 1)

C(5, -5) ⇒ C'(5/4 -9/4, -5/4 +9/4) = C'(-1, 1)