Let's complete the transformation from ABCD to EHGF.
Let's first determine the coordinates of the two figures.
Figure ABCD:
A : -5, 2
B : -3, 4
C : -2, 4
D : -1, 2
Figure EHGF:
E : 4, 1
H : 2, 3
G : 1, 3
F : 0, 1
Reflecting ABCD over the y - axis, we get:
P (x, y) = P' (-x, y)
For ABCD:
A : -5, 2 = A' : 5, 2
B : -3, 4 = B' : 3, 4
C: -2, 4 = C' : 2, 4
D: -1, 2 = D' : 1, 2
Let's now complete the translation,
(x + S), (y + T)
Where,
S = translation at x-axis
T = translation at y-axis
We get,
A' : 5, 2 = E : 4, 1 → S, T = 4 - 5, 1 - 2 = -1, -1
B' : 3, 4 = H : 2, 3 → S, T = 3 - 4, 3 - 4 = -1, -1
C' : 2, 4 = G : 1, 3 → S, T = 1 - 2, 3 - 4 = -1, -1
D' : 1, 2 = F: 0, 1 → S, T = 0 - 1, 1 - 2 = -1, -1
Therefore, we can say that the translation is (x + _, y + _) = (x + (-1), y + (-1)) = x - 1, y - 1
