Question

question
triangle bcd is dilated by a scale factor of \\(\frac{1}{3}\\) to form triangle bcd. side db measures 9. what is the measure of side db?
answer attempt 1 out of 2

Explanation:

Step1: Recall dilation scale factor formula

When a figure is dilated, the length of a side of the image ($D'B'$) is equal to the scale factor ($k$) multiplied by the length of the corresponding side of the original figure ($DB$). The formula is $D'B' = k \times DB$. Here, the scale factor $k = \frac{1}{3}$ and $D'B' = 9$.

Step2: Solve for $DB$

We can rearrange the formula to solve for $DB$. From $D'B' = k \times DB$, we get $DB=\frac{D'B'}{k}$. Substituting the known values, $k = \frac{1}{3}$ and $D'B' = 9$, we have $DB=\frac{9}{\frac{1}{3}}$. When dividing by a fraction, we multiply by its reciprocal, so $DB = 9\times3 = 27$.

Answer:

27