Question

lesson: modeling similar figures in real - world contexts us... a blueprint of a building is 12 inches by 18 inches and needs to be reduced to 6 inches by 9 inches. what is the scale factor? a. 1/4 b. 1/6 c. 1/2 d. 1/3 in manufacturing, why are dilations important? a. to reduce the cost of production b. to speed up the production process c. to ensure that parts of different sizes fit together accurately d. to change the materials used review key concepts

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ for similar figures is given by the ratio of the corresponding side - lengths of the new figure to the original figure. For the length of the blueprint, the original length is 12 inches and the new length is 6 inches. For the width, the original width is 18 inches and the new width is 9 inches. Using the formula $k=\frac{\text{new length}}{\text{original length}}$, for the length: $k=\frac{6}{12}=\frac{1}{2}$, and for the width: $k = \frac{9}{18}=\frac{1}{2}$.

Step2: Analyze dilation in manufacturing

Dilations are important in manufacturing to ensure that parts of different sizes fit together accurately. When parts are scaled up or down (dilated), they need to be in proportion so that they can be assembled correctly. Reducing cost, speeding up the process, or changing materials are not the main reasons related to the concept of dilations.

Answer:

1. C. $\frac{1}{2}$
2. C. To ensure that parts of different sizes fit together accurately.