Math Problem Statement
A line segment has endpoints at (3, 2) and (2, -3). Which reflection will produce an image with endpoints at (3, -2) and (2, 3)?
Solution
Let’s solve this step by step.
Problem Breakdown:
The question asks which reflection will transform the endpoints of a line segment:
- From (3, 2) and (2, -3) to (3, -2) and (2, 3).
Observing the Transformation:
-
The point (3, 2) becomes (3, -2):
- The x-coordinate remains unchanged, but the y-coordinate changes its sign.
- This is a reflection across the x-axis.
-
The point (2, -3) becomes (2, 3):
- Again, the x-coordinate remains the same, and the y-coordinate flips its sign.
- This also matches the reflection across the x-axis.
Conclusion:
The correct answer is:
- A reflection of the line segment across the x-axis.
Let me know if you need further clarification or additional questions to practice.
Relative Questions to Expand Understanding:
- What happens to coordinates during a reflection across the y-axis?
- How do you reflect a point across the line ?
- How do reflections differ from rotations in geometry?
- What is the result of reflecting a point across both the x-axis and the y-axis?
- How do you identify the line of reflection given two sets of points?
Tip:
When reflecting a point, always focus on which coordinate (x or y) is changing to determine the line of reflection.
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Math Problem Analysis
Mathematical Concepts
Geometry
Reflections
Coordinate Plane
Formulas
Reflection across the x-axis: (x, y) → (x, -y)
Theorems
Reflection Theorem
Suitable Grade Level
Grades 8-10