HELP I"LL GIVE BRAINLIEST
The image of a triangle after it has been dilated with a center of dilation at the origin has vertices at A prime(12, –6), B prime(–24, –12), and C prime. If the pre-image of B prime, point B, has coordinates of (–18, –9) and the pre-image of C prime, point C, has coordinates of (–13.5, 18), which statements are true? Check all that apply. The coordinates of C prime are (27, 18). The coordinates of C prime are (–18, 24). The scale factor is 1 and one-third. The scale factor is 1 and one-fifth. The scale factor is Three-fourths. The coordinates of A are (16, –8). The coordinates of A are (9, –4.5).

scale factor is 2/3.  

directions of B are (9,- 27).  

directions of C' are : (12,18)  

Bit by bit clarification:  

The picture of a triangle after it has been widened with a middle at the beginning has vertices at A'(- 12,6) B'(6,- 18) and C' .  

Point A has directions of (- 18,9) and the pre-picture of C' point C has directions of (18,12).  

Unmistakably when we think about point An and point A' we see that the change is an enlargement.  

let the scale factor of widening is 'k'.  

for example A→ A'  

for example k(- 18,9)=(- 12,6)  

(- 18k,9k)=(- 12,6)  

for example - 18k=-12  

also, 9k=6  

Henceforth, on tackling we get:  

k=2/3  

for example the scale factor is 2/3.  

Moreover,  

we discover the directions of B(c,d) by:  

2/3(c,d)=(6,- 18)  since B→ B'  

2/3×c=6  

Subsequently c=9  

furthermore, 2/3 ×d=-18  

d=-27.  

Subsequently, the directions of B are (9,- 27).  

Likewise the directions of C are (18,12)  

Subsequently, directions of C' are:  

which means, the directions of C' are : (12,18)  

answer; i believe the correct answer is (federalist);