Can someone me with this math question. fill all blanks urgent 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)

sine

step-by-step explanation: