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 :
- The -coordinate remains 5.
- The -coordinate changes from to .
Thus, the location of is:
Would you like further clarification or additional examples?
Here are 5 related questions to explore:
- What happens when a point is reflected over the -axis?
- How do reflections affect distances from the axis of reflection?
- Can a point remain unchanged after a reflection? Under what conditions?
- What are the coordinates of a point reflected over the line ?
- 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