Question

the image of a triangle after it has been dilated with a center at the origin has vertices at a, b, and c. if the pre - image of a, point a, has coordinates of (-18, 9) and the pre - image of c, point c, has coordinates of (18, 12), which statements are true? select 3 options. the coordinates of c are (27, 18). the coordinates of c are (12, 8). the scale factor is 1.5. the scale factor is 0.75. the scale factor is \\(\frac{2}{3}\\). the coordinates of b are (9, -27). the coordinates of b are (4, -12).

Explanation:

Step1: Calculate scale factor

Scale factor $k = \frac{A'_x}{A_x} = \frac{-12}{-18} = \frac{2}{3}$

Step2: Verify C' coordinates

$C'_x = 18 \times \frac{2}{3} = 12$, $C'_y = 12 \times \frac{2}{3} = 8$

Step3: Find pre-image B coordinates

$B_x = \frac{B'_x}{k} = \frac{6}{\frac{2}{3}} = 9$, $B_y = \frac{-18}{\frac{2}{3}} = -27$

Answer:

A. The scale factor is $\frac{2}{3}$.
B. The coordinates of B are (9, -27).
C. The coordinates of C' are (12, 8).