△ABC is congruent to △GHE. Describe a sequence of transformations from △ABC to △GHE that proves their congruence.
△ABC:
A = (1, - 3)
B = (1, - 1)
C = (4, - 3)
△GHE:
G = (- 2, 2)
H = (- 4, 2)
E = (- 2, 5)
To prove that △ABC is congruent to △GHE, we can use a sequence of transformations.
1. Translation: Translate △ABC to the left by 3 units and up by 4 units to obtain a new triangle △A'B'C':
A' = (1 - 3, -3 + 4) = (-2, 1)
B' = (1 - 3, -1 + 4) = (-2, 3)
C' = (4 - 3, -3 + 4) = (1, 1)
2. Reflection: Reflect △A'B'C' over the y-axis to obtain a new triangle △A''B''C'':
A'' = (-(-2), 1) = (2, 1)
B'' = (-(-2), 3) = (2, 3)
C'' = (-1, 1)
3. Translation: Translate △A''B''C'' to the left by 4 units and down by 3 units to obtain △GHE:
G = (2 - 4, 1 - 3) = (-2, -2)
H = (2 - 4, 3 - 3) = (-2, 0)
E = (-1 - 4, 1 - 3) = (-5, -2)
Therefore, △ABC is congruent to △GHE.