Point O is the center of dilation. Triangle X Y Z is dilated to create triangle X prime Y prime Z prime. The length of O Z is 2 and the length of Z Z prime is 4. The length of side X prime Y prime is 9 and the length of side Y prime Z prime is 12.
Triangle XYZ was transformed by DO,3. What is the length of side XY? 

1.5
4.5
3
18

We are given that triangle \( XYZ \) is dilated by a scale factor of 3 (\( D_{O,3} \)), and we need to find the length of side \( XY \) of the pre-image triangle before dilation.

### Information provided:
- The scale factor \( k = 3 \) (since it was dilated by \( D_{O,3} \)).
- The length of side \( X'Y' \) (in the dilated triangle) is 9.
  
Since the scale factor of dilation is 3, the sides of the original triangle \( XYZ \) are \( \frac{1}{3} \) of the corresponding sides of the dilated triangle \( X'Y'Z' \).

### Calculation:
To find the length of side \( XY \), we divide the length of the corresponding side \( X'Y' \) by the scale factor:

\[
XY = \frac{X'Y'}{k} = \frac{9}{3} = 3
\]

Thus, the length of side \( XY \) is **3**.

### Answer: 
The correct option is **3**.

Would you like more details or explanations?

Here are 5 related questions:
1. What is the general formula for finding a side length after dilation?
2. How do you determine the center of dilation from coordinates?
3. Can the scale factor be negative, and what does that imply geometrically?
4. If the scale factor was 2, what would the length of side \( XY \) be?
5. What happens to the angles of a triangle when it undergoes dilation?

**Tip:** When dealing with dilation, remember that lengths change by the scale factor, but angles remain the same.

Point O is the center of dilation. Triangle X Y Z is dilated to create triangle X prime Y prime Z prime. The length of O Z is 2 and the length of Z Z prime is 4. The length of side X prime Y prime is 9 and the length of side Y prime Z prime is 12. Triangle XYZ was transformed by DO,3. What is the length of side XY? 1.5 4.5 3 18

Learn how to find the length of side XY of triangle XYZ after dilation with a scale factor of 3. The problem covers geometric transformations, dilation theorems, and the relation between pre-image and image side lengths. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation