Question

problem 4
precisely describe a dilation that takes the smaller figure to the larger figure

Explanation:

Step1: Identify the center of dilation

The center of dilation is point \(C\) (since dilations are centered around a point and visually it seems to be the fixed - point around which the figure is expanding).

Step2: Find the scale factor

Count the distance from the center \(C\) to a vertex of the smaller figure and the distance from the center \(C\) to the corresponding vertex of the larger figure. For example, if we consider a vertex of the smaller figure that is 1 unit away from \(C\) horizontally and 1 unit away from \(C\) vertically, and the corresponding vertex of the larger figure is 3 units away from \(C\) horizontally and 3 units away from \(C\) vertically. The scale factor \(k = 3\) (since the ratio of the distances from the center of dilation to corresponding points on the larger and smaller figures is 3).

Answer:

The dilation has a center at point \(C\) and a scale factor of 3.