Question

1. squares s and q are scaled copies of one another.

a. what scale factor maps square s onto square q?
b. what scale factor maps square q onto square s?
diagram: square s with 1.4 in, square q with 5.6 in

1. will any two squares always be scaled copies of one another? explain.

1. figure b is a scaled copy of figure a with a scale factor of ( 5 \frac{1}{2} ). what is the value of x?

diagram: figure a (small triangle) with side 4, figure b (large triangle) with side x

spiral review

1. select all the ratios that are equivalent to 12 : 3.

□ a. 6:1 □ b. 1:4
□ c. 4:1 □ d. 24:6
□ e. 15:6 □ f. 1,200:300
□ g. 112:13

Explanation:

Problem 6a

Step1: Recall scale factor formula

The scale factor from Square S to Square Q is the length of Q divided by length of S.
Length of S: \( 1.4 \) in, Length of Q: \( 5.6 \) in.

Step2: Calculate scale factor

Scale factor \( = \frac{5.6}{1.4} = 4 \)

Step1: Recall scale factor formula

The scale factor from Square Q to Square S is the length of S divided by length of Q.
Length of S: \( 1.4 \) in, Length of Q: \( 5.6 \) in.

Step2: Calculate scale factor

Scale factor \( = \frac{1.4}{5.6} = \frac{1}{4} \)

All squares have four right angles (90°) and all sides equal. For any two squares, we can find a scale factor by dividing the side length of one square by the side length of the other. Scaling a square's side by a factor will preserve the right angles and equal - side property, so one square can be a scaled copy of the other.

Answer:

4

Problem 6b