Math Problem Statement
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
Solution
We are given that triangle is dilated by a scale factor of 3 (), and we need to find the length of side of the pre-image triangle before dilation.
Information provided:
- The scale factor (since it was dilated by ).
- The length of side (in the dilated triangle) is 9.
Since the scale factor of dilation is 3, the sides of the original triangle are of the corresponding sides of the dilated triangle .
Calculation:
To find the length of side , we divide the length of the corresponding side by the scale factor:
Thus, the length of side is 3.
Answer:
The correct option is 3.
Would you like more details or explanations?
Here are 5 related questions:
- What is the general formula for finding a side length after dilation?
- How do you determine the center of dilation from coordinates?
- Can the scale factor be negative, and what does that imply geometrically?
- If the scale factor was 2, what would the length of side be?
- 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.
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Math Problem Analysis
Mathematical Concepts
Geometry
Dilation
Scale Factor
Formulas
Side length of pre-image = Side length of image / Scale factor
Theorems
Dilation Theorem: A dilation maps a figure to a similar figure, maintaining angle measures and altering side lengths by a constant scale factor
Suitable Grade Level
Grades 8-10