Math Problem Statement

Point JJ is located at left parenthesis, minus, 1, comma, minus, 6, right parenthesis(−1,−6) on the coordinate plane. Point JJ is reflected over the xx-axis to create point J, primeJ ′ . What ordered pair describes the location of J, prime, question markJ ′

Solution

When a point is reflected over the xx-axis, the yy-coordinate of the point changes its sign, while the xx-coordinate remains the same.

Given the coordinates of point JJ as (1,6)(-1, -6):

  1. The xx-coordinate remains 1-1.
  2. The yy-coordinate changes from 6-6 to 66 because of the reflection over the xx-axis.

Thus, the coordinates of the reflected point JJ' are:

J=(1,6)J' = (-1, 6)

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

Here are some related questions you might explore:

  1. How do you reflect a point over the yy-axis?
  2. What is the effect of reflecting a point over the line y=xy = x?
  3. How would you reflect a point over the origin?
  4. What happens to a point's coordinates when it is reflected over the line y=xy = -x?
  5. How do reflections affect the distance between two points on a coordinate plane?

Tip: When reflecting over the xx-axis, always invert the yy-coordinate's sign while keeping the xx-coordinate the same!

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Plane
Reflections

Formulas

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

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-8