ABC is congruent to GHE . Describe a sequence of transformations from ABC to GHE that proves their congruence.

Question

ABC = (1,-3) (1,-1) (4,-3)
GHE = (-2,2) (-4,2) (-2,5)

Answer 1

Here is a possible sequence of transformations:

1. Translation: Translate point GHE by (-3, -5) to obtain G'H'E'.

G'H'E' = (-5,-3) (-7,-3) (-5,0)

2. Reflection: Reflect G'H'E' over the x-axis to obtain G"H"E".

G"H"E" = (-5,3) (-7,3) (-5,0)

3. Rotation: Rotate G"H"E" counterclockwise around the origin by 90 degrees to obtain G""H""E"".

G""H""E"" = (3,5) (3,7) (0,5)

4. Translation: Translate G""H""E"" by (2,1) to obtain GHE.

GHE = (1,6) (1,8) (4,6)

Now, ABC and GHE are congruent.