Question

1. a poster is 4 inches by 6 inches and is enlarged to 12 inches by 18 inches. what is the scale factor?

a. 4
b. 2.5
c. 2
d. 3

1. if a building model is scaled down to 1/50th of the actual size, what is the scale factor?

a. $\frac{1}{25}$
b. $\frac{1}{5}$
c. $\frac{1}{100}$
d. $\frac{1}{50}$

1. what geometric property remains unchanged during a dilation?

a. angles
b. area
c. width
d. length

1. in manufacturing, why are dilations important?

a. to speed up the production process
b. to change the materials used
c. to reduce the cost of production
d. to ensure that parts of different sizes fit together accurately

Explanation:

Step1: Calculate scale factor (Q1)

Scale factor = $\frac{\text{New dimension}}{\text{Original dimension}}$. For length: $\frac{12}{4}=3$, for width: $\frac{18}{6}=3$.

Step2: Identify scale factor (Q2)

Scaled down to $\frac{1}{50}$ of actual size means scale factor = $\frac{1}{50}$.

Step3: Recall dilation properties (Q3)

Dilation preserves angle measures, changes linear dimensions and area.

Step4: Analyze dilation use in manufacturing (Q4)

Dilations create scaled models/parts, ensuring proper fit of sized components.

Answer:

1. d. 3
2. c. $\frac{1}{50}$
3. a. Angles
4. d. To ensure that parts of different sizes fit together accurately