Question

question 3 of 10
what is the scale factor from △rst to △uvw?

a. 3
b. 1
c. 2
d. 0

Explanation:

Step1: Identify Corresponding Sides

In similar triangles, corresponding sides are proportional. For $\triangle RST$ and $\triangle UVW$, let's find corresponding sides. Side $RS = 8$ in $\triangle RST$ and corresponding side $UV = 8$? Wait, no, wait the diagram: Wait, $\triangle RST$ has sides $RS = 8$, $ST = 7$, $RT = 7$? Wait no, maybe I misread. Wait, $\triangle RST$: $RS = 8$, $ST = 7$, $RT = 7$? Wait $\triangle UVW$: $UV = 8$? Wait no, the user's diagram: Wait, maybe the sides: Wait, $\triangle RST$: $RS = 8$, $ST = 7$, $RT = 7$? Wait $\triangle UVW$: $UV = 8$? No, wait the options are 3,1,2,0. Wait maybe the sides: Wait, maybe $\triangle RST$ has a side of 8, and $\triangle UVW$ has a corresponding side of 8? No, that can't be. Wait, maybe I made a mistake. Wait, the scale factor is the ratio of corresponding sides of the image to the original. Wait, $\triangle RST$ to $\triangle UVW$: let's check the sides. Wait, maybe the sides of $\triangle RST$: $RS = 8$, $ST = 7$, $RT = 7$? And $\triangle UVW$: $UV = 8$, $VW = 7$, $UW = 7$? Wait, then all corresponding sides are equal. So the scale factor is $\frac{UV}{RS} = \frac{8}{8} = 1$? Wait, but let's confirm. The scale factor from $\triangle RST$ to $\triangle UVW$ is (length of side in UVW) / (length of corresponding side in RST). If all corresponding sides are equal, then the scale factor is 1. So the answer should be B. 1.

Step2: Calculate Scale Factor

Scale factor $k = \frac{\text{Length of side in } \triangle UVW}{\text{Length of corresponding side in } \triangle RST}$. Let's take side $RS$ (length 8) in $\triangle RST$ and corresponding side $UV$ (length 8) in $\triangle UVW$. Then $k = \frac{8}{8} = 1$. Alternatively, take side $ST$ (length 7) and corresponding side $VW$ (length 7): $k = \frac{7}{7} = 1$. So the scale factor is 1.

Answer:

B. 1