Question

4. Triangle ABC has vertices A(-2, 0), B(0, 3), and C(2, 3) and is dilated by a factor of 2 using

the point (0, -1) as the point of dilation. The dilated triangle is named AA'B'C: What are
the coordinates of the vertices of the resulting triangle?

Answer 1

• A'(-4, 1)
• B'(0, 7)
• C'(4, 7)

Explanation:

When the dilation factor is k and the center of dilation is (a, b), the transformation relation is ...

(x, y) ⇒ (a, b) + k((x, y) -(a, b)) = (kx +(1-k)a, ky +(1-k)b)

For k=2, (a, b) = (0, -1) the transformation is ...

(x, y) ⇒ (2x, 2y +1)

So, the given vertices are dilated to ...

A(-2, 0) ⇒ (2(-2), 2(0)+1) = A'(-4, 1)

B(0, 3) ⇒ (2(0), 2(3)+1) = B'(0, 7)

C(2, 3) ⇒ (2(2), 2(3)+1) = C'(4, 7)