Based on the graph, the composition of translations include the following;
(x, y) → (x' + 5, y' + 1)
(x, y) → (x" - 5, y' - 5).
In Mathematics, a translation is a type of transformation that shifts every point of a geometric object in the same direction on the cartesian coordinate, and for the same distance.
Based on the information provided in the diagram, we have the following coordinates for the pre-image and image:
(x, y) → (x + h, y + k)
A (-4, 2) → A' (1, 3).
For the value of h, we have;
1 = x + h
1 = -4 + h
h = 1 + 4
h = 5 (5 units right)
For the value of k, we have;
3 = y + k
3 = 2 + k
k = 3 - 2
k = 1 (1 unit up).
Therefore, the first translation is (x, y) → (x' + 5, y' + 1)
For the second translation, we have:
(x, y) → (x + h, y + k)
A' (1, 3) → A" (-4, -2).
For the value of h, we have;
-4 = x + h
-4 = 1 + h
h = -4 - 1
h = -5 (5 units left)
For the value of k, we have;
-2 = y + k
-2 = 3 + k
k = -2 - 3
k = -5 (5 units down).
Therefore, the second translation is (x, y) → (x" - 5, y' - 5).