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: Identify corresponding sides

Since Figure Q is a scaled - copy of Figure P, the ratios of corresponding sides are equal. Side AB in Figure P corresponds to side XY in Figure Q, and side CD in Figure P corresponds to side ZW in Figure Q.

Step2: Set up ratio equations

The ratio of the lengths of corresponding sides should be the same. The ratio of AB to CD in Figure P should be equal to the ratio of XY to ZW in Figure Q. That is, $\frac{AB}{CD}=\frac{XY}{ZW}$. Substituting the given values ($AB = 6$, $CD = 3$, $XY = 4$, $ZW=n$), we get $\frac{6}{3}=\frac{4}{n}$. Cross - multiplying gives $6n=12$, so $n = 2$. Also, we can write the equivalent ratios in different forms. The ratio of AB to XY should be equal to the ratio of CD to ZW, i.e., $\frac{6}{4}=\frac{3}{n}$.

Answer:

A. $\frac{6}{3}=\frac{4}{n}$
B. $\frac{6}{4}=\frac{3}{n}$