Question

3 adnan wants a larger garden. he draws △pqr to show his original garden. he wants to enlarge the garden, so he uses a dilation to form the image △pqr. adnan uses vertex p as the center of dilation. a. write a fraction for each quotient of corresponding side lengths. $\frac{pq}{pq}=$__ $\frac{qr}{qr}=$ $\frac{pr}{pr}=$__ b. what do your answers to problem 3a tell you about the scale factor adnan used?

Explanation:

Step1: Find the length of $PQ$ and $PQ'$

$PQ = 8$ ft, $PQ'=12$ ft. So $\frac{PQ'}{PQ}=\frac{12}{8}=\frac{3}{2}$

Step2: Find the length of $QR$ and $Q'R'$

$QR = 6$ ft, $Q'R' = 9$ ft. So $\frac{Q'R'}{QR}=\frac{9}{6}=\frac{3}{2}$

Step3: Find the length of $PR$ and $PR'$

$PR = 10$ ft, $PR'=15$ ft. So $\frac{PR'}{PR}=\frac{15}{10}=\frac{3}{2}$

Step4: Analyze the scale - factor

Since the ratios of all corresponding side - lengths are equal to $\frac{3}{2}$, the scale factor of the dilation is $\frac{3}{2}$.

Answer:

a. $\frac{PQ'}{PQ}=\frac{3}{2}$, $\frac{Q'R'}{QR}=\frac{3}{2}$, $\frac{PR'}{PR}=\frac{3}{2}$
b. The scale factor of the dilation is $\frac{3}{2}$.