Reflection Rule Calculator

Formula

To calculate the reflection of a point:

For reflection in the x-axis: \( R(x, y) = (x, -y) \)
For reflection in the y-axis: \( R(x, y) = (-x, y) \)
For reflection in the line \( y = x \): \( R(x, y) = (y, x) \)

What is a Reflection Rule?

A Reflection Rule in mathematics, specifically in geometry, refers to a transformation that creates a mirror image of a shape or figure across a specific line of reflection. This rule states that each point of the original figure and its image are the same distance from the line of reflection. Essentially, the line of reflection acts as a mirror where the original figure and its reflection are identical in size and shape, but are opposite in orientation.

Example Calculation 1

Let's assume the following values:

Original Point: (3, 4)
Reflection Axis: X-Axis

Using the formula:

\[ R(3, 4) = (3, -4) \]

The reflected point is (3, -4).

Example Calculation 2

Let's assume the following values:

Original Point: (5, -2)
Reflection Axis: Line \( y = x \)

Using the formula:

\[ R(5, -2) = (-2, 5) \]

The reflected point is (-2, 5).