Question

1. there are two scale drawings of the actual dog, which is 4 ft tall.

the 2ft drawing is 1/2 the size of the actual dog. in order to scale the drawing back to being the size of the actual dog, it would be scaled up by a factor of 2. the 2 ft drawing is then known as a 1:2 drawing because it is 1/2 as large as the actual dog.
a. what is the scale factor that created the 6 - in. drawing?

Explanation:

Step1: Convert units

Since \(1\) foot \( = 12\) inches, the actual dog's height \(h_{actual}=4\) ft \(=4\times12 = 48\) inches.

Step2: Calculate scale factor

The scale factor \(k\) is given by the ratio of the drawing size to the actual size. The drawing size \(h_{drawing}=6\) inches. So, \(k=\frac{h_{drawing}}{h_{actual}}\).
Substitute \(h_{drawing} = 6\) and \(h_{actual}=48\) into the formula: \(k=\frac{6}{48}=\frac{1}{8}\).

Answer:

The scale factor is \(\frac{1}{8}\)