Question

lesson 5 practice problems
a. what is the scale factor from s to l?
b. what is the scale factor from l to s?
c. triangle m is also a scaled copy of s. the scale factor from s to m is $\frac{3}{2}$. what is the scale factor from m to s?

Explanation:

Step1: Determine the scale factor from S to L

Assume the base of triangle S is \(2\) units and the base of triangle L is \(6\) units.
The scale factor \(k_{S
ightarrow L}=\frac{\text{length of L}}{\text{length of S}}\)
\(k_{S
ightarrow L}=\frac{6}{2} = 3\)

Step2: Determine the scale factor from L to S

The scale factor \(k_{L
ightarrow S}=\frac{\text{length of S}}{\text{length of L}}\)
Since \(k_{S
ightarrow L} = 3\), then \(k_{L
ightarrow S}=\frac{1}{k_{S
ightarrow L}}\)
\(k_{L
ightarrow S}=\frac{1}{3}\)

Step3: Determine the scale factor from M to S

Given \(k_{S
ightarrow M}=\frac{3}{2}\)
The scale factor \(k_{M
ightarrow S}=\frac{1}{k_{S
ightarrow M}}\)
\(k_{M
ightarrow S}=\frac{2}{3}\)

Answer:

a. \(3\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{3}\)