Question

selecting the correct scale factor
which scale drawing of the parallelogram has a scale factor of \\( \frac { 1 } { 3 } \\), if the original parallelogram has lengths 6 cm and 1.5
cm?

Explanation:

Step1: Calculate the scaled - down lengths

The formula for the scale factor \(k=\frac{\text{scaled length}}{\text{original length}}\). Given \(k = \frac{1}{3}\), and original lengths \(a = 6\mathrm{cm}\) and \(b=15\mathrm{cm}\).
For the first side: \(\text{scaled length}_1=6\times\frac{1}{3}\)

$$6\times\frac{1}{3}=2\mathrm{cm}$$

For the second side: \(\text{scaled length}_2 = 15\times\frac{1}{3}\)

$$15\times\frac{1}{3}=5\mathrm{cm}$$

Step2: Check each parallelogram

• First parallelogram: The lengths are \(2\mathrm{cm}\) and \(5\mathrm{cm}\)
• Second parallelogram: If we assume wrong scale factor calculations (not relevant as we found the correct one)
• Third parallelogram: If we assume wrong scale factor calculations (not relevant as we found the correct one)
• Fourth parallelogram: If we assume wrong scale factor calculations (not relevant as we found the correct one)

Answer:

The first parallelogram (with side lengths \(2\mathrm{cm}\) and \(5\mathrm{cm}\)) is the correct scale drawing.