Question

parallelogram qrst is dilated by a scale factor of 2 to form parallelogram qrst. side st measures 18. what is the measure of side st?

Explanation:

Step1: Recall the dilation formula

When a figure is dilated, the length of a side of the new figure ($l_{new}$) is related to the length of the corresponding side of the original figure ($l_{original}$) by the formula $l_{new}=k\times l_{original}$, where $k$ is the scale factor. Here, $k = 2$, $l_{new}=S'T'=18$, and we want to find $l_{original}=ST$.

Step2: Solve for the original side length

From $l_{new}=k\times l_{original}$, we can rewrite it as $l_{original}=\frac{l_{new}}{k}$. Substitute $k = 2$ and $l_{new}=18$ into the formula: $ST=\frac{S'T'}{2}$.
$$ST=\frac{18}{2}=9$$

Answer:

$9$