1. What Is Reflection In Mathematics?

Reflection is a transformation that produces a mirror image of a point, line, or shape across a specified axis. In coordinate geometry, reflection creates a symmetrical point with respect to either the x-axis or y-axis.

2. How Does Reflection Calculation Work?

The calculator uses simple reflection formulas:

Where:

• x — The original x-coordinate
• y — The original y-coordinate

Explanation: Reflection preserves the distance from the axis but changes the sign of the coordinate perpendicular to that axis.

3. Applications Of Reflection

Details: Reflection transformations are fundamental in computer graphics, architectural design, physics (especially optics), and various engineering applications where symmetry is important.

4. Using The Calculator

Tips: Enter the original x and y coordinates, select the axis of reflection (x-axis or y-axis), and click calculate to see the reflected coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What happens when reflecting over both axes?
A: Reflecting over both axes transforms (x, y) to (-x, -y), which is equivalent to a 180-degree rotation about the origin.

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 decimal values for both x and y coordinates with up to 4 decimal places precision.

Q4: What is the distance between original and reflected points?
A: The distance between original and reflected points is twice the distance from the original point to the axis of reflection.

Q5: How is reflection used in real-world applications?
A: Reflection is used in computer graphics, mirror design, satellite dish construction, and in various optical instruments where precise mirroring is required.