Math Problem Statement

Identify and plot the point that is an x-axis reflection of the point in Figure 1 and the y-axis reflection of the point in Figure 2.

Solution

The task involves reflecting points across the x-axis and y-axis based on the given points in Figures 1 and 2.

Reflection Instructions:

  1. X-Axis Reflection:

    • A reflection over the x-axis changes the y-coordinate of a point to its opposite (multiply by -1), while the x-coordinate remains unchanged.

    • In Figure 1, there is a red point at coordinates (-4, 3). The x-axis reflection of this point will change the y-coordinate from 3 to -3, keeping the x-coordinate the same:

      • Reflection: (-4, -3).
  2. Y-Axis Reflection:

    • A reflection over the y-axis changes the x-coordinate of a point to its opposite (multiply by -1), while the y-coordinate remains unchanged.

    • In Figure 2, there is a red point at coordinates (-4, 3). The y-axis reflection will change the x-coordinate from -4 to 4, keeping the y-coordinate the same:

      • Reflection: (4, 3).

Summary:

  • X-axis reflection of (-4, 3) (from Figure 1) is (-4, -3).
  • Y-axis reflection of (-4, 3) (from Figure 2) is (4, 3).

Would you like further clarification, or help plotting the reflected points?

Relative Questions:

  1. How would you reflect a point across the origin?
  2. What would be the reflection of a point across the line y=xy = x?
  3. How does the reflection across the x-axis affect the quadrant in which the point lies?
  4. If you reflect a point over both axes, what is the transformation?
  5. Can a point remain unchanged after a reflection? Under what circumstances?

Tip:

Always remember: in reflections, only one coordinate changes sign depending on the axis you reflect over (x-axis for y, y-axis for x).

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Reflections

Formulas

Reflection over x-axis: (x, y) -> (x, -y)
Reflection over y-axis: (x, y) -> (-x, y)

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-9