Question

which is the scale factor proportion for the enlargement shown?
(image: small parallelogram with height 1 in., base 2 in.; larger parallelogram with height x in., base 6 in. (not drawn to scale))
options:

• \\(\frac{1}{x} = \frac{2}{6}\\)
• \\(\frac{1}{x} = \frac{6}{2}\\)
• \\(\frac{1}{6} = \frac{2}{x}\\)
• (partial: 1 6)

Explanation:

Step1: Understand Scale Factor

Scale factor for enlargement means the ratio of corresponding sides of the original figure to the enlarged figure should be equal. The original figure has sides 1 in (height) and 2 in (base). The enlarged figure has height \( x \) in and base 6 in.

Step2: Set Up Proportion

The ratio of original height to enlarged height should equal the ratio of original base to enlarged base. So, \(\frac{\text{Original Height}}{\text{Enlarged Height}}=\frac{\text{Original Base}}{\text{Enlarged Base}}\), which is \(\frac{1}{x}=\frac{2}{6}\).

Answer:

$\boldsymbol{\frac{1}{x}=\frac{2}{6}}$ (First option)