Question

figure abcdef is a dilation of figure abcdef.
a. label the center of dilation and explain how you found it.
b. what is the scale factor of the dilation?
c. write a similarity statement.

Explanation:

Step1: Identify the center of dilation

The center of dilation is the point that remains fixed during the dilation. By observing the figure, we can see that the corresponding points of the original figure \(ABCDEF\) and the dilated figure \(A'B'C'D'E'F'\) are aligned such that the lines connecting them meet at a common point. This point is the center of dilation.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. Let's consider the vertical side \(AB\) and \(A'B'\). Suppose the length of \(AB\) is \(2\) units (counting the grid squares) and the length of \(A'B'\) is \(4\) units. Then the scale factor \(k=\frac{\text{length of }A'B'}{\text{length of }AB}=\frac{4}{2} = 2\)

Step3: Write the similarity statement

If two figures are similar, we can write a similarity statement. For dilation, the original figure \(ABCDEF\) and the dilated figure \(A'B'C'D'E'F'\) are similar. The similarity statement is \(ABCDEF\sim A'B'C'D'E'F'\)

Answer:

a. The center of dilation is the point where the lines connecting corresponding vertices (e.g., \(A - A'\), \(B - B'\), etc.) intersect.
b. The scale factor is \(2\) (assuming a side - length ratio of \(2:1\) as calculated above).
c. \(ABCDEF\sim A'B'C'D'E'F'\)