Question

interactive practice: understand dilations and similarity
jake drew the figures below on a piece of paper. he says that figure efgh is dilated by a scale factor of 3 to form figure efgh. he also says that the center of dilation is point d.
which mistake did jake make, if any?
the scale factor is wrong. it should be less than 1.
what is the scale factor?
$\frac{1}{4}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{3}{4}$

Explanation:

Step1: Recall dilation concept

Dilation is a transformation that changes the size of a figure. If the scale - factor $k$ is between 0 and 1, the figure is reduced. If $k>1$, the figure is enlarged.

Step2: Observe the figures

Figure $E'F'G'H'$ is smaller than figure $EFGH$. So the scale - factor should be less than 1. Let's find the ratio of corresponding side lengths.

Step3: Measure side lengths

Suppose we measure the horizontal side of $EFGH$ and $E'F'G'H'$. Let's assume the length of a horizontal side of $EFGH$ is 3 units and the length of the corresponding horizontal side of $E'F'G'H'$ is 1 unit.
The scale - factor $k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}$.
If we take a side of $E'F'G'H'$ and the corresponding side of $EFGH$, say the horizontal side of $E'F'$ and $EF$. If the length of $EF = 3$ and the length of $E'F'=1$, then the scale - factor $k=\frac{1}{3}$.

Answer:

The mistake Jake made is that the scale factor is wrong. It should be less than 1. The scale factor is $\frac{1}{3}$.