Math Problem Statement

Point GG is located at left parenthesis, 5, comma, minus, 1, right parenthesis(5,−1) on the coordinate plane. Point GG is reflected over the xx-axis to create point G, primeG ′ . What ordered pair describes the location of G, prime, question markG ′ ?

Solution

When a point is reflected over the x-axis, the x-coordinate remains the same, while the y-coordinate is negated.

The original point G(5,1)G(5, -1):

  • The xx-coordinate remains 5.
  • The yy-coordinate changes from 1-1 to 11.

Thus, the location of GG' is:

G(5,1)G'(5, 1)

Would you like further clarification or additional examples?

Here are 5 related questions to explore:

  1. What happens when a point is reflected over the yy-axis?
  2. How do reflections affect distances from the axis of reflection?
  3. Can a point remain unchanged after a reflection? Under what conditions?
  4. What are the coordinates of a point reflected over the line y=xy = x?
  5. How do multiple reflections (e.g., over both axes) affect a point's location?

Tip: Always check the axis being reflected over to determine which coordinate changes!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Reflections on the Coordinate Plane

Formulas

Reflection over the x-axis: (x, y) → (x, -y)

Theorems

Reflection Property: The distance from the original point to the axis of reflection equals the distance from the reflected point to the axis.

Suitable Grade Level

Grades 6-8