1. What Is Reflection In Geometry?

Reflection is a transformation that flips a figure across a line, creating a mirror image. The line is called the line of reflection, and the distance from the original figure to the line equals the distance from the reflected figure to the line.

2. How Does Reflection Work?

Reflection preserves the shape and size of the original figure but reverses its orientation. Points on the line of reflection remain fixed, while other points are mapped to their mirror positions.

3. Reflection Rules Explained

The calculator uses these reflection rules:

Where:

• (x, y) — Original coordinates
• (x, -y) — Result after x-axis reflection
• (-x, y) — Result after y-axis reflection

Explanation: X-axis reflection changes the sign of the y-coordinate while keeping the x-coordinate unchanged. Y-axis reflection changes the sign of the x-coordinate while keeping the y-coordinate unchanged.

4. Using The Reflection Calculator

Tips: Enter the x and y coordinates of your point, select the reflection axis (x or y), and click Calculate. The calculator will show both the resulting coordinates and the reflection rule used.

5. Frequently Asked Questions (FAQ)

Q1: What happens when a point is reflected over both axes?
A: Reflecting over both x and y axes results in (x, y) → (-x, -y), which is equivalent to a 180° rotation about the origin.

Q2: Do reflections preserve distance and angle measurements?
A: Yes, reflections are isometries - they preserve distances between points and angles between lines.

Q3: How do I reflect shapes with multiple points?
A: Apply the same reflection rule to each vertex of the shape, then connect the reflected points in the same order.

Q4: What is the line of reflection?
A: The line of reflection is the perpendicular bisector of the segment connecting each point to its reflected image.

Q5: Can this calculator handle decimal coordinates?
A: Yes, the calculator accepts and processes decimal coordinates with up to 4 decimal places of precision.