1. What Is Reflection In Geometry?

Reflection is a transformation that flips a point or shape across a line (axis), creating a mirror image. In coordinate geometry, reflection changes the sign of either the x or y coordinate while keeping the other coordinate unchanged.

2. How Does Reflection Work?

The reflection formulas are:

Where:

• (x, y) — Original coordinates
• (x, -y) — Reflection over x-axis
• (-x, y) — Reflection over y-axis

Explanation: Reflection preserves distance and creates congruent shapes, making it an isometric transformation.

3. Applications Of Reflection

Details: Reflection is used in computer graphics, architecture, physics (light reflection), and symmetry analysis in mathematics and art.

4. Using The Calculator

Tips: Enter the x and y coordinates of your point, 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: Does reflection change the size of shapes?
A: No, reflection is an isometric transformation that preserves distances, angles, and sizes of shapes.

Q3: How is reflection different from rotation?
A: Reflection creates a mirror image, while rotation turns the shape around a fixed point by a specific angle.

Q4: Can I reflect over lines other than the axes?
A: Yes, but the formulas are more complex. This calculator focuses on reflection over the x and y axes.

Q5: What are real-world examples of reflection?
A: Mirror images, symmetrical building designs, light reflection in optics, and computer graphics transformations.