Question

q3 - mathematics gr 8 - section 1 | lesson: modeling similar figures in real-world contexts using transformations

1. a rectangle that is 5 inches by 8 inches is scaled down by a factor of 0.5.

what are the new dimensions?
a. 3 inches by 5 inches
b. 2.5 inches by 5 inches
c. 2.5 inches by 4 inches
d. 3 inches by 4 inches

1. what is the ratio called that determines how much a figure is enlarged or reduced during a dilation?

a. proportional ratio
b. scale factor
c. enlargement ratio
d. dilation ratio

1. how are similar figures related in terms of their angles and sides?

a. angles and sides are the same
b. angles are different, and sides are the same
c. angles and sides are different
d. angles are the same, and sides are proportional

1. when a rectangle measuring 5 inches by 8 inches is enlarged to 20 inches by 32 inches, what is the scale factor?

a. 5
b. 3
c. 4
d. 2

Explanation:

Step1: Scale down rectangle dimensions

Multiply each original dimension by 0.5:
New width: $5 \times 0.5 = 2.5$ inches
New length: $8 \times 0.5 = 4$ inches

Step2: Identify dilation ratio term

Recall the definition of the ratio for dilation.

Step3: Recall similar figures properties

Use the definition of similar figures for angles and sides.

Step4: Calculate enlargement scale factor

Divide new dimension by original dimension:
$\frac{20}{5} = 4$ or $\frac{32}{8} = 4$

Answer:

1. c. 2.5 inches by 4 inches
2. b. Scale factor
3. d. Angles are the same, and sides are proportional
4. c. 4