As shown in the graph, ΔGHI ≅ ΔG'H'I', since this is a vertical shift, and ΔG'H'I' ≅ ΔG''H''I'', since this is a horizontal shift.

We can also show that triangles GHI and G''H''I'' are congruent directly, by using the translation
A) (x, y) → (x + 3, y - 4).
B) (x, y) → (x - 3, y + 1).
C) (x, y) → (x + 2, y + 2).
D) (x, y) → (x + 4, y - 5).

If a point A(x, y) is translated by 'h' units to the right and 'k' units vertically down, coordinates of the image point will be A'(x + h, y - k).

Rule of translation for triangle GHI to form ΔG"H"I" will be Option (D).

Coordinates of G → (-4, 4)

If point G is translated 'h' units horizontally right and 'k' units down,

Coordinates of the image point G" → (-4 + h, 4 - k)

From the graph attached,

Coordinates of G" → (0, -1)

Since, both the coordinates of G" are same.

Therefore, (-4 + h) = 0

h = 4

And (4 - k) = -1

k = 4 + 1

k = 5

Therefore, ΔGHI will be translated by 4 units right and 5 units down on the graph.

Rule defining the translation will be, Option (D) (x, y) → (x + 4, y - 5)

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