Enter the original point and the axis of reflection into the calculator to determine the reflected point.

Reflection Rule Formula

The following formula is used to calculate the coordinates of a point after reflection.

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)Variables:

  • R(x, y) is the reflected point
  • (x, y) is the original point

To calculate the reflection of a point in the x-axis, keep the x-coordinate the same and change the sign of the y-coordinate. For reflection in the y-axis, change the sign of the x-coordinate and keep the y-coordinate the same. For reflection in the line y = x, swap the x and y coordinates.

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.

How to Calculate Reflection Rule?

The following steps outline how to calculate the Reflection Rule using the given formula:

  1. First, determine the type of reflection (x-axis, y-axis, or line y = x).
  2. Next, identify the original point (x, y).
  3. Apply the corresponding formula to calculate the reflected point (R(x, y)).
  4. Finally, determine the coordinates of the reflected point (R(x, y)).
  5. After applying the formula and calculating the result, check your answer with the given examples.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Type of reflection: Reflection in the x-axis

Original point (x, y) = (3, 5)

Apply the formula: R(x, y) = (x, -y)

Reflected point (R(x, y)) = (3, -5)