Math Problem Statement

Given a line of reflection at x=2, which of the following is the image of the point (2,3)?

Solution

When reflecting a point across a vertical line, the line of reflection acts as a mirror. In this case, the line of reflection is x=2x = 2.

Given the point (2,3)(2,3):

  • The x-coordinate of the point is already 22, which is on the line of reflection.
  • When a point lies directly on the line of reflection, its image remains the same.

Thus, the image of the point (2,3)(2,3) after reflecting across the line x=2x = 2 is (2,3)(2,3).

Would you like further explanation or have any questions about this reflection process?

Here are 5 related questions for further exploration:

  1. What is the image of the point (5,3)(5,3) after reflecting over the line x=2x = 2?
  2. How do you reflect a point across the y-axis?
  3. What would be the image of (4,1)(4, -1) after reflecting across the line x=2x = 2?
  4. How do you find the line of reflection if the original point and its image are given?
  5. Can you describe how to reflect a point over the line y=3y = 3?

Tip: When reflecting a point, the distance from the point to the line of reflection is the same as the distance from the image to the line of reflection.

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Math Problem Analysis

Mathematical Concepts

Geometry
Reflection across a line

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12