Triangle EFG is dilated by a scale factor of 3 centered at (0, 1) to create triangle E'F'G'. Which statement is true about the dilation?

E (0,5) F (1,1) H (1,1) G (-2,1)

segment EH and segment E prime H prime both pass through the center of dilation.

The slope of segment EF is the same as the slope of segment E prime H prime.

segment E prime G prime will overlap segment EG.

segment EH ≅ segment E prime H prime.

The slope of segment EF is the same as the slope of segment E prime H prime.

Step-by-step explanation:

The center of dilation is located at (0,1) and E is located at (0,5), then, x-coordinate of E' is 0.

The distance between E and the center of dilation is 5-1 = 4

The distance between E' and the center of dilation has to be 3*4 = 12

Therefore, E' is located at (0,13)

The center of dilation is located at (0,1) and H is located at (1,1), then, y-coordinate of H' is 1.

The distance between H and the center of dilation is 1-0 = 1

The distance between H' and the center of dilation has to be 3*1 = 3

Therefore, H' is located at (3,1)

slope of segment EF = (1 - 5) / (1 - 0) = - 4

slope of segment E'H' = (1 - 13) / (3 - 0) = - 4