1. What Is Point Reflection?

Point reflection is a transformation that flips a point across a specific axis (x-axis or y-axis) on a coordinate plane. This geometric operation creates a mirror image of the original point.

2. How Does Reflection Work?

The reflection formulas are:

Explanation: When reflecting over the x-axis, the x-coordinate remains the same while the y-coordinate changes sign. When reflecting over the y-axis, the y-coordinate remains the same while the x-coordinate changes sign.

3. Applications Of Reflection

Details: Point reflection is fundamental in computer graphics, physics (especially optics), engineering design, and geometric proofs. It's also essential for understanding symmetry in mathematics.

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 distance from the origin?
A: No, reflection preserves distance from the origin. Only the position relative to the axes changes.

Q3: Can I reflect shapes or just points?
A: You can reflect entire shapes by reflecting each individual point that defines the shape.

Q4: How is reflection different from rotation?
A: Reflection creates a mirror image, while rotation turns the point around a fixed center by a specific angle.

Q5: What's the difference between reflection and translation?
A: Reflection flips the point across an axis, while translation moves the point a fixed distance in a specific direction without changing its orientation.