ABC is congruent to GHE . Describe a sequence of transformations from ABC to GHE that proves their congruence.
ABC = (1,-3) (1,-1) (4,-3)
GHE = (-2,2) (-4,2) (-2,5)
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.