Answer:Δ ABC was dilated by a scale factor of 1/2, reflected across the y-axis and moved through the translation (3 , 2)Step-by-step explanation:* Lets explain how to solve the problem- The similar triangles have equal ratios between their corresponding side- So lets find from the graph the corresponding sides and calculate the ratio, which is the scale factor of the dilation- In Δ ABC : ∵ The length of the horizontal line is x2 - x1- Let A is (x1 , y1) and B is (x2 , y2)∵ A = (-4 , -2) and B = (0 , -2)∴ AB = 0 - -4 = 4- The corresponding side to AB is ED∵ The length of the horizontal line is x2 - x1- Let E is (x1 , y1) , D is (x2 , y2)∵ E = (5 , 1) and D = (3 , 1)∵ DE = 5 - 3 = 2∵ Δ ABC similar to Δ EDF∵ ED/AB = 2/4 = 1/2∴ The scale factor of dilation is 1/2* Δ ABC was dilated by a scale factor of 1/2- From the graph Δ ABC in the third quadrant in which x-coordinates of any point are negative and Δ EDF in the first quadrant in which x-coordinates of any point are positive∵ The reflection of point (x , y) across the y-axis give image (-x , y)* Δ ABC is reflected after dilation across the y-axis- Lets find the images of the vertices of Δ ABC after dilation and reflection and compare it with the vertices of Δ EDF to find the translation∵ A = (-4 , -2) , B = (0 , -2) , C (-2 , -4)∵ Their images after dilation are A' = (-2 , -1) , B' = (0 , -1) , C' = (-1 , -2)∴ Their image after reflection are A" = (2 , -1) , B" = (0 , -1) , C" = (1 , -2)∵ The vertices of Δ EDF are E = (5 , 1) , D = (3 , 1) , F = (4 ,0)- Lets find the difference between the x-coordinates and the y- coordinates of the corresponding vertices∵ 5 - 2 = 3 and 1 - -1 = 1 + 1 = 2∴ The x-coordinates add by 3 and the y-coordinates add by 2∴ Their moved 3 units to the right and 2 units up* The Δ ABC after dilation and reflection moved through the translation (3 , 2)