Math Problem Statement

The query submitted by the user:

Solution

To solve the problem, we need to reflect each of the given points across the x-axis. When reflecting a point (x,y)(x, y) across the x-axis, the x-coordinate remains the same, while the y-coordinate changes its sign.

Let's apply this to each point:

  1. Point (7, -2):

    • Reflection: (7,2)(7, 2)
  2. Point (-3, 9):

    • Reflection: (3,9)(-3, -9)
  3. Point (3, -9):

    • Reflection: (3,9)(3, 9)
  4. Point (-2, -7):

    • Reflection: (2,7)(-2, 7)

So the reflections of the points are:

  1. (7, -2) → (7, 2)
  2. (-3, 9) → (-3, -9)
  3. (3, -9) → (3, 9)
  4. (-2, -7) → (-2, 7)

Would you like more details on the reflection process or have any further questions?

Additional Questions:

  1. How would you reflect points across the y-axis?
  2. What would the reflection of a point across the origin look like?
  3. If a point lies on the x-axis, what is its reflection across the x-axis?
  4. How does reflecting a point over both axes affect its coordinates?
  5. Can you describe how to reflect a point over the line y=xy = x?

Tip:

Remember that reflecting a point across the x-axis only changes the sign of the y-coordinate, while reflecting across the y-axis only changes the sign of the x-coordinate.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9