For solving this, we need to find the values of the coordinates for A, B, C, and D.
In this case, we have that:
A (2, 1)
B (6, 1)
C (6, 3)
D (2, 3)
Then, we have the rule of the transformation (a Translation):
(x, y) ---> (x + 2, y - 3). That is, this rule tells us' two units to the right and 3 units downward.
Thus, for each coordinate in the preimage ABCD, we will have an image A'B'C'D'.
Therefore:
Having the point A (2, 1), applying the rule of transformation, we have:
(2, 1) ---> (2 + 2, 1 -3) = (4, -2)
Point B:
(6, 1) ---> (6 + 2, 1 - 3) = (8, -2)
Point C:
(6, 3) ---> (6 + 2, 3 - 3) = (8, 0)
Point D:
(2, 3) ---> (2 + 2, 3 - 3) = (4, 0)
Then, the coordinates for the image is:
A'(4, -2)
B'(8, -2)
C'(8, 0)
D'(4, 0)
Therefore, after the transformation ( a translation ), we have that the coordinates for the image of the quadrilateral are:
A'(4, -2), B'(8, -2), C'(8, 0), D'(4, 0).