Reflection Calculator Examples

Reflection Calculation:

\[ R(x, y) = (x, -y) \text{ (reflection over x-axis)} \] \[ R(x, y) = (-x, y) \text{ (reflection over y-axis)} \] \[ R(x, y) = (-x, -y) \text{ (reflection over origin)} \]

Reflected Coordinates:

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1. What Is Reflection In Geometry?

Reflection is a transformation that flips a figure across a line (the axis of reflection) to create a mirror image. In coordinate geometry, reflection changes the sign of one or both coordinates depending on the axis of reflection.

2. How Reflection Calculation Works

The calculator uses these reflection formulas:

\[ R_x(x, y) = (x, -y) \text{ (reflection over x-axis)} \] \[ R_y(x, y) = (-x, y) \text{ (reflection over y-axis)} \] \[ R_o(x, y) = (-x, -y) \text{ (reflection over origin)} \]

Where:

\( (x, y) \) — Original coordinates
\( R_x \) — Reflection over x-axis
\( R_y \) — Reflection over y-axis
\( R_o \) — Reflection over origin

Explanation: Reflection creates a mirror image by changing the sign of coordinates relative to the axis of reflection.

3. Applications Of Reflection

Details: Reflection is used in computer graphics, architecture, physics (light reflection), and various engineering applications where symmetry is important.

4. Using The Reflection Calculator

Tips: Enter the original coordinates (x, y) and select the reflection axis. The calculator will compute and display the reflected coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between reflection and rotation?
A: Reflection creates a mirror image across an axis, while rotation turns a figure around a fixed point by a certain angle.

Q2: Can reflection change the size of a figure?
A: No, reflection is an isometric transformation that preserves distances and angles, so the size remains unchanged.

Q3: How does reflection over the origin work?
A: Reflection over the origin is equivalent to a 180-degree rotation around the origin, changing the sign of both coordinates.

Q4: What are real-world examples of reflection?
A: Mirrors, symmetrical building designs, Rorschach inkblot tests, and many natural phenomena exhibit reflection symmetry.

Q5: Can I reflect over any line, not just the axes?
A: Yes, but the calculation is more complex. This calculator focuses on reflections over the coordinate axes and origin.