Question

vwxyz ~ ghdef. find wx and ef.
write your answers as decimals or whole numbers.
wx =
ef =

Explanation:

Step1: Find the scale factor

First, we identify corresponding sides. Let's take \( VZ = 35 \) and \( DE = 5 \). The scale factor from \( GHDEF \) to \( VWXYZ \) is \( \frac{VZ}{DE}=\frac{35}{5} = 7 \).

Step2: Find \( WX \)

The corresponding side to \( WX \) in \( GHDEF \) is \( GH = 4 \)? Wait, no, wait. Wait, \( GHDEF \) has sides: \( GH = 4 \), \( HD = 2 \), \( DE = 5 \), \( EF =? \), \( FG = 5 \). Wait, \( VWXYZ \) has \( VW = 28 \), \( VZ = 35 \), \( ZY = 42 \), \( YX =? \), \( XW =? \). Wait, let's match the order. Since \( VWXYZ \sim GHDEF \), the order of the letters matters. So \( V \) corresponds to \( G \), \( W \) to \( H \), \( X \) to \( D \), \( Y \) to \( E \), \( Z \) to \( F \)? Wait, no, maybe \( V \) corresponds to \( G \), \( W \) to \( H \), \( X \) to \( D \), \( Y \) to \( E \), \( Z \) to \( F \)? Wait, let's check the sides. \( VZ \) in \( VWXYZ \) and \( GF \) in \( GHDEF \)? Wait, no, the given sides: \( VW = 28 \), \( VZ = 35 \), \( ZY = 42 \). In \( GHDEF \), \( GH = 4 \), \( HD = 2 \), \( DE = 5 \), \( EF =? \), \( FG = 5 \). Wait, maybe \( V \) corresponds to \( G \), \( W \) to \( H \), \( X \) to \( D \), \( Y \) to \( E \), \( Z \) to \( F \). So \( VW \) corresponds to \( GH \), \( WX \) to \( HD \), \( XY \) to \( DE \), \( YZ \) to \( EF \), \( ZV \) to \( FG \). Let's check the scale factor. \( VW = 28 \), \( GH = 4 \), so scale factor \( k=\frac{VW}{GH}=\frac{28}{4}=7 \). Then \( WX \) corresponds to \( HD = 2 \), so \( WX = k\times HD = 7\times2 = 14 \). Now \( EF \) corresponds to \( YZ = 42 \), so \( EF=\frac{YZ}{k}=\frac{42}{7}=6 \)? Wait, no, wait. Wait, if \( VWXYZ \sim GHDEF \), then the ratio of corresponding sides is equal. So \( \frac{VW}{GH}=\frac{WX}{HD}=\frac{XY}{DE}=\frac{YZ}{EF}=\frac{ZV}{FG} \). We have \( VW = 28 \), \( GH = 4 \), so \( \frac{28}{4}=7 \). Then \( WX \) corresponds to \( HD = 2 \), so \( \frac{WX}{2}=7 \), so \( WX = 14 \). Then \( YZ = 42 \) corresponds to \( EF \), so \( \frac{42}{EF}=7 \), so \( EF = \frac{42}{7}=6 \). Wait, let's verify with \( VZ = 35 \) and \( FG = 5 \). \( \frac{35}{5}=7 \), which matches the scale factor. And \( ZY = 42 \), \( EF \) is what we found as 6, \( \frac{42}{6}=7 \), correct. And \( XY \) corresponds to \( DE = 5 \), so \( XY = 7\times5 = 35 \), which we can check, but we don't need that. So \( WX = 14 \), \( EF = 6 \).

Answer:

\( WX = 14 \)
\( EF = 6 \)