Question

2 figure f is a scaled copy of figure e. we know: ab = 6 cd = 3 xy = 4 zw = a select all true equations. a 6/3 = 4/a b 6/4 = 3/a c 3/4 = 6/a d 6/3 = a/4 e 6/4 = a/3 f 3/4 = a/6

Explanation:

Step1: Determine the scale factor

Since Figure \( f \) is a scaled copy of Figure \( e \), the ratios of corresponding lengths are equal. The corresponding lengths are \( AB = 6 \) and \( XY = 4 \), \( CD = 3 \) and \( ZW=a \).
The ratio of \( AB \) to \( XY \) is \(\frac{AB}{XY}=\frac{6}{4}\), and the ratio of \( CD \) to \( ZW \) is \(\frac{CD}{ZW}=\frac{3}{a}\).

Step2: Set up the proportion

Because of the property of scaled - copies (similarity), \(\frac{AB}{XY}=\frac{CD}{ZW}\). Substituting the values, we get \(\frac{6}{4}=\frac{3}{a}\).
Cross - multiply: \(6\times a = 4\times3\), \(6a = 12\), \(a = 2\).
Also, from \(\frac{CD}{AB}=\frac{ZW}{XY}\), \(\frac{3}{6}=\frac{a}{4}\). Cross - multiply: \(3\times4=6\times a\), \(12 = 6a\), \(a = 2\).

Answer:

B. \(\frac{6}{4}=\frac{3}{a}\), F. \(\frac{3}{4}=\frac{a}{6}\)