1. What Is Reflection Over Y-Axis?

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

2. How Does The Calculator Work?

The calculator uses the reflection formula:

Where:

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

Explanation: The transformation preserves the vertical position of the point while mirroring it horizontally across the y-axis.

3. Importance Of Reflection In Geometry

Details: Reflection is a fundamental transformation in geometry used in symmetry analysis, computer graphics, and various engineering applications. Understanding reflections helps in visualizing how shapes behave under transformations.

4. Using The Calculator

Tips: Enter the x and y coordinates of your point. The calculator will instantly compute and display both the original point and its reflection across the y-axis.

5. Frequently Asked Questions (FAQ)

Q1: What happens to points exactly on the y-axis?
A: Points on the y-axis (where x=0) remain unchanged after reflection since -0 = 0.

Q2: How does reflection affect shapes?
A: Reflection creates a mirror image of the original shape. The shape's size and orientation are preserved, but it appears flipped horizontally.

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

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

Q5: How is reflection used in real-world applications?
A: Reflection transformations are used in computer graphics, architecture, physics (especially optics), and various design fields where symmetry is important.