Question

2 figure q is a scaled copy of figure p.
we know:
· ab = 6
· cd = 3
· xy = 4
· zw = n
select all true equations.
a $\frac{6}{3}=\frac{4}{n}$
b $\frac{6}{4}=\frac{3}{n}$
c $\frac{3}{4}=\frac{6}{n}$
d $\frac{6}{3}=\frac{n}{4}$
e $\frac{6}{4}=\frac{n}{3}$
f $\frac{3}{4}=\frac{n}{6}$

Explanation:

Step1: Find the scale factor

Since Figure \(Q\) is a scaled copy of Figure \(P\), the ratios of corresponding lengths are equal.
The corresponding lengths are \(AB = 6\) and \(XY=4\), \(CD = 3\) and \(ZW=n\).
The ratio of \(AB\) to \(XY\) is \(\frac{AB}{XY}=\frac{6}{4}\), and the ratio of \(CD\) to \(ZW\) is \(\frac{CD}{ZW}=\frac{3}{n}\).
Since the scale factor is the same for all corresponding lengths in a scaled - copy, we can set up the proportion \(\frac{6}{4}=\frac{3}{n}\) (by cross - multiplying \(6n = 4\times3\)).
Also, from the proportion \(\frac{CD}{AB}=\frac{ZW}{XY}\), we have \(\frac{3}{6}=\frac{n}{4}\) (by cross - multiplying \(6n=3\times4\)).

Step2: Check each option

• Option A: \(\frac{6}{3}=\frac{4}{n}\), cross - multiplying gives \(6n = 3\times4\), \(n = 2\). But from \(\frac{6}{4}=\frac{3}{n}\), \(n = 2\) is correct.
• Option B: \(\frac{6}{4}=\frac{3}{n}\), cross - multiplying gives \(6n=4\times3\), \(n = 2\).
• Option C: \(\frac{3}{4}=\frac{6}{n}\), cross - multiplying gives \(3n = 24\), \(n = 8\). Incorrect.
• Option D: \(\frac{6}{3}=\frac{n}{4}\), cross - multiplying gives \(3n=24\), \(n = 8\). Incorrect.
• Option E: \(\frac{6}{4}=\frac{n}{3}\), cross - multiplying gives \(4n = 18\), \(n=\frac{9}{2}\). Incorrect.
• Option F: \(\frac{3}{4}=\frac{n}{6}\), cross - multiplying gives \(4n = 18\), \(n=\frac{9}{2}\). Incorrect.

Answer:

A. \(\frac{6}{3}=\frac{4}{n}\), B. \(\frac{6}{4}=\frac{3}{n}\)