Math Problem Statement

The point HH is plotted on the coordinate grid below. Plot the point H, primeH ′ , the reflection of HH over the xx-axis

Solution

To reflect a point H(x,y)H(x, y) over the xx-axis, you can follow these steps:

Reflection Process:

  1. Keep the xx-coordinate the same.
  2. Change the sign of the yy-coordinate.

Thus, the reflection of the point H(x,y)H(x, y) over the xx-axis would be H(x,y)H'(x, -y).

Example:

If the point H(x,y)H(x, y) has specific coordinates, let's say H(a,b)H(a, b), then the reflection HH' will be located at H(a,b)H'(a, -b).

If you can provide the coordinates of the point HH, I can help you calculate the exact reflection. Would you like to provide that information, or perhaps upload an image of the grid so I can assist more directly?


Related Questions:

  1. What happens when you reflect a point over the yy-axis instead of the xx-axis?
  2. How do you reflect a point over both axes simultaneously?
  3. Can you reflect a point over a line other than the axes, such as y=xy = x?
  4. How does reflection change the orientation of shapes on a coordinate grid?
  5. What is the general rule for reflecting a point over the line y=xy = -x?

Tip: Reflections over the axes preserve distances but reverse the direction along one axis.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Reflections

Formulas

Reflection formula: H'(x, -y)

Theorems

Reflection across the x-axis theorem

Suitable Grade Level

Grades 6-8