MATH SOLVE

2 months ago

Q:
# I need help with this math question. Can you fill all the blanks please

Accepted Solution

A:

Answer: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)