Triangle abc was translated according to the rule (x, y) → (x + 1.5, y – 3.5) to create the image δa'b'c' shown on the coordinate plane. which graph shows the pre-image, δabc? coordinates are c (-5,-10), b(-1,-1),a(-1,2)

Given:
ΔA'B'C' image.
A (-1,2)
B (-1,-1)
C (-5,-10)

rule of translation(x,y) → (x + 1.5,y - 3.5)

This means that the given coordinates are the the sum of x and the difference of y.

A:
-1 = x + 1.5  →  -x = 1.5 + 1 → -x = 2.5 → -x/-1 = 2.5/-1 → x = -2.5
2 = y - 3.5 → -y = -3.5 - 2 → -y = -5.5 → -y/-1 = -5.5/-1 → y = 5.5
A (-2.5 , 5.5)

B:
-1 =  x + 1.5  →  -x = 1.5 + 1 → -x = 2.5 → -x/-1 = 2.5/-1 → x = -2.5
-1 = y - 3.5 → -y = -3.5 + 1 → -y = -2.5 → -y/-1 = -2.5/-1 → y = 2.5
B (-2.5,2.5)

C: 
-5 = x + 1.5 → -x = 1.5 + 5 → -x = 6.5 → -x/-1 = 6.5/-1 → x = -6.5
-10 = y - 3.5 → -y = -3.5 + 10 → -y = 6.5 → -y/-1 = 6.5/-1 → y = -6.5
C (-6.5, -6.5)

The pre image will have the following coordinates:
A (-2.5 , 5.5) ; B (-2.5,2.5) ; C (-6.5, -6.5)