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)
