Triangle ABC was dilated and translated to form similar triangle A'B'C'. What is the scale factor of the dilation?A. 1/5B. 2/5C. 5/2D. 5/1

The scale factor of dilation from ABC to A’B’C’ is 2.5.Step-by-step explanation:Step 1:First, we plot the coordinates of both triangles.The coordinates of triangle ABC are as follows;A = (0, 2), B = (2, 2), and C = (2,0).The coordinates of triangle A’B’C’ are;A’= (-4, -1), B’= (1, -1), and C’ = (1, -6).Step 2: Next, we need to find the distances between at least to coordinates for both triangles.The distances between vertical lines are found by calculating the difference in y values while for horizontal lines, the distances are found by calculating the difference between the x values.The distance of AB = 2 - 0 = 2 units, the distance of BC = 2 - 0 = 2 units.The distance of A’B’ = 1 - (-4) = 5 units, the distance of B’C’ = 6 - 1 = 5 units (both points are negative y)Step 3:To calculate the scale factor, we divide the measurement after scaling by the same measurement before scaling. In this case, it is the length of the AB. So the scale factor = [tex]\frac{5}{2}[/tex] = 2.5.The scale factor for line BC = [tex]\frac{5}{2}[/tex] = 2.5.