Question

1) △ABC has A(-2,-2), B(-1,2) and C(2,1). After a dilation centered at the origin, △A'B'C' has A'(-4,-4), B'(-2,4) and C'(4,2). What is the scale

factor of the dilation?
a) -2
C) 2
b) -1/2
d) 1/2

Answer 1

Option (C)

Explanation:

If a point is dilated by a scale factor of 'k' about the origin,

Rule for the dilation,

(x, y) → (kx, ky)

By this rule, if ΔABC is dilated to form image triangle as ΔA'B'C',

A(-2, -2) → A'[2×(-2), 2×(-2)]

B(-1, 2) → B'[2×(-1), 2×(2)]

C(2, 1) → C'[2×(2), 2×(1)]

Therefore, scale factor of the dilation of the dilation will be k = 2

Option (C) will be the answer.