Question

the quotients of the corresponding side lengths in figures jklm and pqrs are shown below the figures. is figure jklm a dilation of figure pqrs? choose one option from each drop - down menu to answer the question. in figures jklm and pqrs, the quotient of sides jk and pq is equivalent to choose... therefore, the quotients of the corresponding side lengths of the figures show that figure jklm choose... a dilation of figure pqrs because choose... of the quotients are equivalent.

the side lengths of jklm are: j to k is 30 mm, k to l is 21 mm, l to m is 10 mm, m to j is 24 mm. the side lengths of pqrs are: p to q is 24 mm, q to r is 15 mm, r to s is 8 mm, s to p is 18 mm.

the quotients are: $\frac{jk}{pq}=\frac{30}{24}$, $\frac{kl}{qr}=\frac{21}{15}$, $\frac{lm}{rs}=\frac{10}{8}$, $\frac{mj}{sp}=\frac{24}{18}$

Explanation:

Step1: Simplify the quotient of JK and PQ

$\frac{JK}{PQ}=\frac{30}{24}=\frac{5}{4}$

Step2: Simplify the quotient of KL and QR

$\frac{KL}{QR}=\frac{21}{15}=\frac{7}{5}$

Step3: Compare the quotients

Since $\frac{5}{4}
eq\frac{7}{5}$, not all quotients of corresponding - side lengths are equal.

Answer:

In figures JKLM and PQRS, the quotient of sides JK and PQ is equivalent to $\frac{5}{4}$. Therefore, the figure JKLM is not a dilation of figure PQRS because not all of the quotients are equivalent.