1. What Is Reflection Over Y = X?

Reflection over the line y = x is a transformation that swaps the x and y coordinates of a point. This transformation creates a mirror image of the original point across the line y = x.

2. How Does The Calculator Work?

The calculator uses the reflection formula:

Where:

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

Explanation: The reflection swaps the coordinates, placing the x-value in the y-position and the y-value in the x-position.

3. Importance Of Reflection Calculation

Details: Reflection over y = x is fundamental in geometry, computer graphics, and various mathematical applications. It's particularly important in matrix transformations and symmetry analysis.

4. Using The Calculator

Tips: Enter the x and y coordinates of your point. 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 their x and y coordinates are equal.

Q2: How does reflection over y = x relate to matrix operations?
A: Reflection over y = x can be represented by the matrix \[ \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \] when multiplying coordinate vectors.

Q3: What is the inverse of reflection over y = x?
A: Reflection over y = x is its own inverse. Applying the reflection twice returns the point to its original position.

Q4: How does this relate to function inverses?
A: The graph of a function and its inverse are reflections of each other across the line y = x.

Q5: Can this calculator handle decimal coordinates?
A: Yes, the calculator accepts and accurately processes decimal coordinates with up to 4 decimal places.