Question

1. modeling real life you are making a blueprint of a house. you measure the lengths of the walls of a room to be 11 feet by 12 feet. when you draw the room on the blueprint, the lengths of the walls are 8.25 inches by 9 inches. what scale factor dilates the room to the blueprint?

Explanation:

Step1: Convert feet to inches

Since 1 foot = 12 inches,
Original length 1: $11 \times 12 = 132$ inches
Original length 2: $12 \times 12 = 144$ inches

Step2: Calculate scale factor

Scale factor = $\frac{\text{Blueprint length}}{\text{Actual length}}$
Using first pair: $\frac{8.25}{132} = \frac{3}{48} = \frac{1}{16}$
Verify with second pair: $\frac{9}{144} = \frac{1}{16}$

Answer:

The scale factor is $\frac{1}{16}$ (1 inch on blueprint = 16 inches in real life, or 1 inch = $1\frac{1}{3}$ feet)