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)
