Question

The image of a triangle after it has been dilated with a center at the origin has vertices at A prime(–12, 6), B prime(6, –18), and C prime. If the pre-image of A prime, point A, has coordinates of (–18, 9) and the pre-image of C prime, point C, has coordinates of (18, 12), which statements are true? Select 3 options.
The coordinates of C prime are (27, 18).
The coordinates of C prime are (12, 8).
The scale factor is 1.5.
The scale factor is 0.75.
The scale factor is Two-thirds.
The coordinates of B are (9, –27).
The coordinates of B are (4, –12).

Answer 1

True statements (3):

- The coordinates of C prime are (12, 8).
- The scale factor is Two-thirds.
- The coordinates of B are (9, −27).

Reason: k = A'/A = (−12)/(−18) = 6/9 = 2/3. Then C' = (18,12)*(2/3) = (12,8). And B = B'/(2/3) = (6,−18)*(3/2) = (9,−27).