Question

a. eduardo uses a scale - factor of 3 to draw figure l. complete figure l by showing the missing sides. b. eduardo uses a scale - factor of 1/3 to draw figure l. complete figure l by showing the missing sides. a wallpaper designer draws figure c as the original figure in a wallpaper pattern. then they draw figures d and e. the center of dilation is point f. which figures, if any, are dilations of figure c? show your work

Explanation:

Step1: Recall dilation definition

A dilation is a transformation that changes the size of a figure but not its shape. If a figure is a dilation of another with center of dilation \(F\), then the ratios of the corresponding distances from \(F\) to the points on the figures are equal.

Step2: Check figure D

Measure the distances from point \(F\) to corresponding vertices of figure \(C\) and figure \(D\). If the ratio of these distances is constant for all corresponding vertices, then figure \(D\) is a dilation of figure \(C\). Let the distance from \(F\) to a vertex \(V_1\) of figure \(C\) be \(d_1\) and the distance from \(F\) to the corresponding vertex \(V_2\) of figure \(D\) be \(d_2\). If \(\frac{d_2}{d_1}=k\) (a constant), then it is a dilation.

Step3: Check figure E

Similarly, measure the distances from point \(F\) to corresponding vertices of figure \(C\) and figure \(E\). Calculate the ratios of these distances. If the ratio is the same for all corresponding vertices, then figure \(E\) is a dilation of figure \(C\).

Answer:

Check the ratios of the distances from point \(F\) to corresponding vertices of figure \(C\) and the other figures. If the ratios are constant for a figure, then that figure is a dilation of figure \(C\). Without specific distance - measurements, we cannot definitively say which figures (if any) are dilations. But the method to determine is by calculating the ratios of distances from the center of dilation \(F\) to corresponding vertices.