Question

1. figure 1 and figure 2 are similar and have the measurements shown in units.

figure 1
figure 2
based on the figures, which proportion is true?
$\frac{x}{y} = \frac{3}{5}$
$\frac{x}{y} = \frac{2}{4}$
$\frac{x}{y} = \frac{4}{2}$
$\frac{x}{y} = \frac{5}{3}$
clear all

Explanation:

Step1: Find the scale factor of similar figures

For similar figures, corresponding sides are proportional. First, find the ratio of corresponding sides of Figure 1 and Figure 2. Take the vertical sides: \( \frac{2}{1.2}=\frac{5}{3}=\frac{4}{2.4}=\frac{5}{3} \) (simplify \( \frac{2}{1.2}=\frac{20}{12}=\frac{5}{3} \), \( \frac{4}{2.4}=\frac{40}{24}=\frac{5}{3} \)).

Step2: Determine the ratio of \( x \) and \( y \)

Since \( x \) is a side of Figure 1 and \( y \) is the corresponding side of Figure 2, the ratio \( \frac{x}{y} \) should be equal to the scale factor of Figure 1 to Figure 2. The scale factor is \( \frac{5}{3} \) (from Step 1, as \( 5 \) is a side of Figure 1 and \( 3 \) is the corresponding side of Figure 2), so \( \frac{x}{y}=\frac{5}{3} \).

Answer:

\(\boldsymbol{\frac{x}{y}=\frac{5}{3}}\) (the option with \( \frac{x}{y}=\frac{5}{3} \))