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:

  1. 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.
  2. 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:

  1. What happens to coordinates during a reflection across the y-axis?
  2. How do you reflect a point across the line y=xy = x?
  3. How do reflections differ from rotations in geometry?
  4. What is the result of reflecting a point across both the x-axis and the y-axis?
  5. 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