A single transformation that takes shape A to shape B is a dilation by a scale factor of -1/2 centered at point (6, 5).
In this exercise, we would have to dilate the coordinates of the preimage by using a scale factor of -1/2 centered at the point (6, 5) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For one of the coordinates of figure A, we have;
Coordinates = (1, 1) → (-1/2(1 - 6) + 6, -1/2(1 - 5) + 5)
Coordinates = (3, 8) → (5/2 + 6, 2 + 5)
Coordinates = (17/2, 7).
Coordinates = (8.5, 7).
In this context, we can logically deduce that a dilation by a scale factor of -1/2 centered at point (6, 5) is a single transformation that maps shape A to shape B.