An algebraic rule to describe this transformation is (x, y) → (x - 2, y - 5). Quadrilateral MNOP was shifted to the left 2 units and 5 units down to produce its image.
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:
(x, y) → (x + h, y + k)
M (-2, 3) → M' (-4, -2).
-4 = x + h
-4 = -2 + h
h = -4 + 2
h = -2 (2 units left)
-2 = y + k
-2 = 3 + k
k = -2 - 3
k = -5 (5 units down).
Therefore, an algebraic rule to describe this transformation is (x, y) → (x - 2, y - 5). In this context, we can logically deduce that quadrilateral MNOP was shifted to the left 2 units and 5 units down to produce its image, quadrilateral M'N'O'P'.