Question

what number can you multiply each distance in the scale drawing by to find the actual distance?

Explanation:

Step1: Analyze the scale ratio

Given the scale \(3\ cm:1.5\ km\). We need to find the multiplier \(x\) such that if the scale - drawing distance is \(d_{sd}\) (in cm) and the actual distance is \(d_{a}\) (in km), then \(d_{a}=x\times d_{sd}\).
From the scale \(3\ cm\) (scale - drawing distance) corresponds to \(1.5\ km\) (actual distance). Let \(x\) be the multiplier. We know that \(d_{a}=x\times d_{sd}\), substituting \(d_{sd} = 3\) and \(d_{a}=1.5\), we get the equation \(1.5=x\times3\).

Step2: Solve for \(x\)

Using the formula \(x=\frac{d_{a}}{d_{sd}}\). Substitute \(d_{a} = 1.5\) and \(d_{sd}=3\) into the formula. Then \(x=\frac{1.5}{3}\).

$$x = 0.5$$

Answer:

\(0.5\)