Math Problem Statement

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

Solution

When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is multiplied by -1.

The original point is M(1,−1)M(1, -1).

Reflecting it over the x-axis:

  • The x-coordinate remains 1.
  • The y-coordinate becomes −(−1)=1-(-1) = 1.

Therefore, the coordinates of the reflected point M′M' are (1,1)(1, 1).

The ordered pair for M′M' is (1,1)(1, 1).

Would you like more details on reflections, or have any other questions?

Here are 5 related questions:

  1. What happens when a point is reflected over the y-axis?
  2. How would the coordinates change if the point was reflected over the line y=xy = x?
  3. What is the result of reflecting a point over both the x-axis and y-axis?
  4. How can you calculate the distance between a point and its reflection over the x-axis?
  5. What would be the coordinates of M′M' if the original point was (1,2)(1, 2)?

Tip: Reflections over different axes follow simple rules, making them easy to perform with practice!

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Reflections

Formulas

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

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-8

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