Rotate A Point 180 Degrees Calculator

Rotating a point 180 degrees around another point is a common geometric transformation. This calculator helps you find the new coordinates of a point after a 180-degree rotation.

How to Use This Calculator

To rotate a point 180 degrees around another point:

Enter the original coordinates of the point you want to rotate (X₁, Y₁)
Enter the coordinates of the center point (X₂, Y₂) around which you want to rotate
Click the "Calculate" button
The calculator will display the new coordinates after rotation

The calculator will also show you a visualization of the rotation.

Formula Explained

To rotate a point (X₁, Y₁) 180 degrees around another point (X₂, Y₂), use the following formulas:

New X-coordinate = 2 × X₂ - X₁

New Y-coordinate = 2 × Y₂ - Y₁

This formula works because a 180-degree rotation is equivalent to reflecting the point through the center point.

Worked Example

Let's say you want to rotate the point (3, 5) 180 degrees around the point (1, 2).

Using the formula:

New X = 2 × 1 - 3 = -1

New Y = 2 × 2 - 5 = -1

The rotated point will be at (-1, -1).

Frequently Asked Questions

What does rotating a point 180 degrees mean?: Rotating a point 180 degrees around another point means flipping it through that point, creating a mirror image across the center point.
Can I rotate a point around itself?: Yes, rotating a point around itself (using the same coordinates for both points) will result in the same coordinates since the point doesn't move.
Is there a difference between rotating 180 degrees and reflecting over a point?: Yes, while both operations result in the same coordinates, they are considered different transformations in geometry.
Can I rotate multiple points at once?: This calculator works with one point at a time. For multiple points, you would need to run the calculation for each point individually.