Question

Suppose the rectangle ABCD is dilated to A'B'C'D by a scale factor of 1/3 with a centet of dilation at the origin. what is the distance from the center of dilation to the midpoint of A'B

Answer 1

Dilation results to enlargement or reduction of the original figure. If the scale factor is less that 1, the result is reduction. Looking at the graph, each small box represents a unit. The origin is the point where the vertical and horizontal lines meet. The distance from the midpoint of AB to the origin is 3 boxes. This means 3 units. Since the dilation was done with a scale factor of 1/3, then the distance of the midpoint of A'B' to the origin would be

1/3 * 3 = 1

the distance from the center of dilation to the midpoint of A'B​ is 1 unit