Answer:
Δ ABC was dilated by a scale factor of 1/2, reflected across the x-axis
and moved through the translation (4 , 1)
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 vertical line is y2 - y1
- Let C is (x1 , y1) and B is (x2 , y2)
∵ B = (-2 , 0) and C = (-2 , -4)
∴ CB = 0 - -4 = 4
- The corresponding side to BC is FE
∵ The length of the vertical line is y2 - y1
- Let F is (x1 , y1) , E is (x2 , y2)
∵ E = (3 , 3) and F = (3 , 1)
∵ FE = 3 - 1 = 2
∵ Δ ABC similar to Δ DEF
∵ FE/BC = 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 y-coordinates
of any point are negative and Δ DFE in the first quadrant in which
y-coordinates of any point are positive
∵ The reflection of point (x , y) across the x-axis give image (x , -y)
* Δ ABC is reflected after dilation across the x-axis
- Lets find the images of the vertices of Δ ABC after dilation and
reflection and compare it with the vertices of Δ DFE to find the
translation
∵ A = (-4 , -2) , B = (-2 , 0) , C (-2 , -4)
∵ Their images after dilation are A' = (-2 , -1) , B' = (-1 , 0) , C' = (-1 , -2)
∴ Their image after reflection are A" = (-2 , 1) , B" = (-1 , 0) , C" = (-1 , 2)
∵ The vertices of Δ DFE are D = (2 , 2) , F = (3 , 1) , E = (3 , 3)
- Lets find the difference between the x-coordinates and the
y- coordinates of the corresponding vertices
∵ 2 - -2 = 4 and 2 - 1 = 1
∴ The x-coordinates add by 4 and the y-coordinates add by 1
∴ Their moved 4 units to the right and 1 unit up
* The Δ ABC after dilation and reflection moved through the
translation (4 , 1)
