### Dilation and Similarity in Triangles**Exercise 9.6.40**A dilation maps ΔDFG onto ΔD'F'G'. Find the missing values.Given data:- $DE' = 4 \, \text{in}$- $DF' = 8 \, \text{in}$- $FG = 9 \, \text{in}$- $FG' = \_\_ \, \text{in}$- $DG = 8 \, \text{in}$- $DG' = \_\_ \, \text{in}$**Instructions:**Simplify your answers.**Procedure:**To find the missing lengths $FG'$ and $DG'$, identify the scale factor of the dilation. Compare the given side lengths of the original triangle and the dilated triangle.1. Calculate the scale factor $k$ using the known side lengths:\[k = \frac{DF'}{DF} = \frac{8}{4}\]Thus, the scale factor $k = 2$.2. Use the scale factor to find the missing lengths:\[FG' = FG \times k = 9 \times 2 = 18 \, \text{in}\]\[DG' = DG \times k = 8 \times 2 = 16 \, \text{in}\]So, the final values are:- FG' = 18 in- DG' = 16 in**Note:**You would typically enter these results in the corresponding fields on the educational platform and then click "Check Answer" to verify.#### Enter your answer in the edit fields and then click Check Answer.---This explanation includes the step-by-step methodology on how to find the required side lengths using dilation and similarity principles in triangles. Remember to enter your calculated answers for $FG'$ and $DG'$ in the provided fields before submitting.

Name: ### Dilation and Similarity in Triangles**Exercise 9.6.40**A dilation
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Description: ### Dilation and Similarity in Triangles**Exercise 9.6.40**A dilation maps ΔDFG onto ΔD'F'G'. Find the missing values.Given data:- $DE' = 4 \, \text{in}$- $DF' = 8 \, \text{in}$- $FG = 9 \, \text{in}$- $FG' = \_\_ \, \text{in}$- \(DG = 8 \,

Given: A dilation map from triangle DFG onto triangle D'F'G'. Given values are DF = 4 in…

Answered: 9.6.40 D'F=8 in FG'= DF= 4 in A…

Math

Geometry

9.6.40 D'F=8 in FG'= DF= 4 in A dilation maps ADFG onto AD'F'G'. Find the missing values. FG=9 in in DG = 8 in D'G'= in DF = 4-in D'F =8 in FG 9 in F'G'= in DG = 8 in D'G" in (Simplify your answers.)

Elementary Geometry For College Students, 7e

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ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

### Dilation and Similarity in Triangles

**Exercise 9.6.40**

A dilation maps ΔDFG onto ΔD'F'G'. Find the missing values.

Given data:
- $DE' = 4 \, \text{in}$
- $DF' = 8 \, \text{in}$
- $FG = 9 \, \text{in}$
- $FG' = \_\_ \, \text{in}$
- $DG = 8 \, \text{in}$
- $DG' = \_\_ \, \text{in}$

**Instructions:**
Simplify your answers.

**Procedure:**
To find the missing lengths $FG'$ and $DG'$, identify the scale factor of the dilation. Compare the given side lengths of the original triangle and the dilated triangle.

1. Calculate the scale factor $k$ using the known side lengths:
\[
k = \frac{DF'}{DF} = \frac{8}{4}
\]
Thus, the scale factor $k = 2$.

2. Use the scale factor to find the missing lengths:
\[
FG' = FG \times k = 9 \times 2 = 18 \, \text{in}
\]
\[
DG' = DG \times k = 8 \times 2 = 16 \, \text{in}
\]

So, the final values are:
- FG' = 18 in
- DG' = 16 in

**Note:**
You would typically enter these results in the corresponding fields on the educational platform and then click "Check Answer" to verify.

#### Enter your answer in the edit fields and then click Check Answer.

---
This explanation includes the step-by-step methodology on how to find the required side lengths using dilation and similarity principles in triangles. Remember to enter your calculated answers for $FG'$ and $DG'$ in the provided fields before submitting.

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