1. What is Reflection Across X-Axis?

Reflection across the x-axis is a geometric transformation that flips a point or shape over the x-axis. The x-coordinate remains the same while the y-coordinate changes sign.

2. How Does the Calculator Work?

The calculator uses the reflection formula:

Where:

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

Explanation: The reflection transformation preserves the x-coordinate while inverting the sign of the y-coordinate, creating a mirror image across the x-axis.

3. Importance of Reflection Calculation

Details: Reflection calculations are fundamental in geometry, computer graphics, physics, and engineering. They help understand symmetry properties and are used in various applications from game development to architectural design.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What happens to a point on the x-axis when reflected?
A: Points on the x-axis (y=0) remain unchanged after reflection since -0 = 0.

Q2: How does reflection affect distance from the origin?
A: Reflection preserves the distance from the origin. The reflected point will be the same distance from the origin as the original point.

Q3: Can this calculator handle decimal coordinates?
A: Yes, the calculator supports both integer and decimal coordinates with high precision.

Q4: What's the difference between reflection across x-axis and y-axis?
A: Reflection across x-axis changes (x,y) to (x,-y), while reflection across y-axis changes (x,y) to (-x,y).

Q5: How are reflections used in real-world applications?
A: Reflections are used in computer graphics, mirror imaging, symmetry analysis in physics, and various engineering applications involving wave propagation and optics.