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, creating a mirror image of the original figure.

2. How Reflection Over Y-Axis Works

The mathematical formula for reflecting a point over the y-axis is:

Where:

• \( x \) — Original x-coordinate
• \( y \) — Original y-coordinate
• \( -x \) — Reflected x-coordinate (sign changed)
• \( y \) — Reflected y-coordinate (unchanged)

Explanation: This transformation creates a mirror image where points on the right side of the y-axis move to the left side, and vice versa, while maintaining the same vertical position.

3. Applications Of Reflection

Details: Reflection transformations are fundamental in computer graphics, game development, architectural design, and physics simulations. They're used to create symmetrical patterns, simulate mirror effects, and solve geometric problems.

4. Using The Calculator

Tips: Enter the x and y coordinates of any point to calculate its reflection over the y-axis. The calculator will show both the original point and its reflected counterpart.

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 differ from rotation?
A: Reflection creates a mirror image across an axis, while rotation turns the point around a fixed center by a specific angle.

Q3: Can this calculator handle decimal coordinates?
A: Yes, the calculator accepts and accurately processes decimal values for both x and y coordinates.

Q4: How is reflection over y-axis different from reflection over x-axis?
A: Reflection over x-axis transforms (x, y) to (x, -y), while reflection over y-axis transforms (x, y) to (-x, y).

Q5: Are there real-world applications of this transformation?
A: Yes, reflection is used in mirror imaging, symmetrical design, computer graphics, and in understanding wave behavior in physics.