Question

select the answers from the drop - down menus to correctly complete the sentences. triangle lmn is a reduction of triangle rst. the scale factor of the dilation is

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ of a dilation from a larger triangle to a smaller triangle is given by the ratio of the corresponding side - lengths of the smaller triangle to the larger triangle.

Step2: Choose corresponding sides

Let's take the side of length $2$ in $\triangle LMN$ and the side of length $8$ in $\triangle RST$. The scale factor $k=\frac{\text{side in }\triangle LMN}{\text{corresponding side in }\triangle RST}$.

Step3: Calculate the scale factor

If we take the ratio of the side - lengths, for example, if we consider the sides of length $2$ (in $\triangle LMN$) and $8$ (in $\triangle RST$), then $k = \frac{2}{8}=\frac{1}{4}=0.25$. If we consider the sides of length $2.5$ (in $\triangle LMN$) and $10$ (in $\triangle RST$), then $k=\frac{2.5}{10} = 0.25$. If we consider the sides of length $3$ (in $\triangle LMN$) and $12$ (in $\triangle RST$), then $k=\frac{3}{12}=0.25$.
Since $0.25=\frac{1}{4}$, $\triangle LMN$ is a reduction of $\triangle RST$ and the scale factor of the dilation is $0.25$.

Answer:

$\triangle LMN$ is a reduction of $\triangle RST$ and the scale factor of the dilation is $0.25$.