1. What is Reflection Over Y = X?

Reflection over y = x is a geometric transformation that swaps the x and y coordinates of a point. The line y = x acts as a mirror, reflecting points across this diagonal line.

2. How Does the Calculator Work?

The calculator uses the reflection formula:

Where:

• \( x \) — Original x-coordinate
• \( y \) — Original y-coordinate

Explanation: The transformation simply swaps the x and y values of the coordinate pair, creating a mirror image across the line y = x.

3. Importance of Reflection Calculation

Details: Reflection transformations are fundamental in geometry, computer graphics, and various mathematical applications. Understanding reflection over y = x is crucial for symmetry analysis and coordinate transformations.

4. Using the Calculator

Tips: Enter the x and y coordinates of the point you want to reflect. The calculator will instantly compute and display the reflected coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What happens to points that lie on the line y = x?
A: Points on the line y = x remain unchanged after reflection, as they are their own mirror images.

Q2: How does reflection over y = x affect geometric shapes?
A: The reflection swaps the x and y coordinates of all vertices, effectively mirroring the shape across the line y = x.

Q3: Is reflection over y = x the same as a 90-degree rotation?
A: No, reflection over y = x is different from rotation. Reflection creates a mirror image, while rotation turns the figure around a point.

Q4: Can this calculator handle decimal coordinates?
A: Yes, the calculator accepts and accurately processes decimal coordinate values.

Q5: What are some practical applications of reflection over y = x?
A: This transformation is used in computer graphics, game development, architectural design, and various mathematical modeling applications.