For a figure on a coordinate plane with the origin as the center of dilation, if (x, y) ⟶ (ax, ay) and (1.5, 2.0) ⟶ (6.0, 8.0), what is a?

The correct answer to this question is 4.

In order to solve this problem, first make an image on your mind how the image is dilated.

The coordinate points at first is (1.5, 2.0). After dilation from the origin, the points became (6.0, 8.0)

Looking at it in fraction form, (new / old) we have
6.0 / 1.5 = 4.0
8.0 / 2.0 = 4.0

The quotient of each fraction yields to 4.0. This means that a = 4.