Question

ariana uses a flag in a shadow play. the distance between the flag and the screen changes.
when the distance changes, the shadow represented by figure defg forms figure defg.
two figures that have the same shape, but not necessarily the same size, are called similar
what is the distance between the corresponding sides of the figures?
de is as long as de.
ef is as ef.

Explanation:

Step1: Determine the scale factor

Assume the scale factor of the dilation is the same for all corresponding sides. Count the length of \(DE\) and \(D'E'\) on the grid. Let's assume \(DE = 4\) units (by counting grid - squares) and \(D'E'=2\) units. The scale factor \(k\) from \(DEFG\) to \(D'E'F'G'\) is \(k=\frac{D'E'}{DE}\).

$$k = \frac{2}{4}=\frac{1}{2}$$

Step2: Apply the scale factor to \(EF\)

Since the figures are similar (by the definition of dilation in a shadow - play, which creates similar figures), the ratio of corresponding sides is the same. Let \(EF\) be a side of the original figure and \(E'F'\) be the corresponding side of the dilated figure. Using the scale factor \(k=\frac{1}{2}\), we have \(E'F'=\frac{1}{2}\times EF\)

Answer:

\(E'F'\) is \(\frac{1}{2}\) as long as \(EF\)