1. What is Reflection Over a Line?

Reflection over a line is a geometric transformation that produces a mirror image of a point across a given line. The reflected point is equidistant from the line but on the opposite side.

2. How Does the Calculator Work?

The calculator uses the reflection formula:

Where:

• \( Line Point \) — A point on the reflection line
• \( Point \) — The original point to be reflected
• \( Point' \) — The reflected point

Explanation: This formula calculates the mirror image of a point across a line defined by a given point on that line.

3. Applications of Reflection

Details: Reflection transformations are used in computer graphics, physics (light reflection), engineering design, and various mathematical applications involving symmetry.

4. Using the Calculator

Tips: Enter the coordinates of a point on the reflection line and the coordinates of the point you want to reflect. The calculator will compute the coordinates of the reflected point.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between reflection over a point and reflection over a line?
A: Reflection over a point produces a point symmetric about that point, while reflection over a line produces a mirror image across that line.

Q2: Can this calculator handle 3D reflections?
A: No, this calculator is designed for 2D reflections over a line in a plane.

Q3: What if the line is not defined by a single point?
A: For reflection over a line, you need at least one point on the line. The direction of the line is not needed for point reflection calculations.

Q4: How accurate are the results?
A: The results are mathematically precise based on the input coordinates, rounded to 4 decimal places for clarity.

Q5: Can I use this for multiple points?
A: Yes, you can calculate the reflection of multiple points over the same line by entering each point separately.