Ineed with this math question. can you fill all the blanks

Δ ABC was dilated by a scale factor of 1/3, reflected across the y-axis

and moved through the translation (1 , -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 vertical line is y2 - y1

- Let A is (x1 , y1) and B is (x2 , y2)

∵ A = (-6 , 0) and B = (-6 , 3)

∴ AB = 3 - 0 = 3

- The corresponding side to AB is FE

∵ The length of the vertical line is y2 - y1

- Let F is (x1 , y1) , E is (x2 , y2)

∵ F = (3 , -2) and E = (3 , -1)

∵ FE = -1 - -2 = -1 + 2 = 1

∵ Δ ABC similar to Δ FED

∵ FE/AB = 1/3

∴ The scale factor of dilation is 1/3

* Δ ABC was dilated by a scale factor of 1/3

- From the graph Δ ABC in the second quadrant in which x-coordinates

 of any point are negative and Δ FED in the fourth 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 FED to find the

 translation

∵ A = (-6 , 0) , B = (-6 , 3) , C (-3 , 0)

∵ Their images after dilation are A' = (-2 , 0) , B' = (-2 , 1) , C' = (-1 , 0)

∴ Their image after reflection are A" = (2 , 0) , B" = (2 , 1) , C" = (1 , 0)

∵ The vertices of ΔFED are F = (3 , -2) , E = (3 , -1) , D = (2 , -2)

- Lets find the difference between the x-coordinates and the

 y- coordinates of the corresponding vertices

∵ 3 - 2 = 1 and -2 - 0 = -2

∴ The x-coordinates add by 1 and the y-coordinates add by -2

∴ Their moved 1 unit to the right and 2 units down

* The Δ ABC after dilation and reflection moved through the

  translation (1 , -2)

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step-by-step explanation:

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