Rotate 90 Degrees Clockwise About The Origin Calculator

This calculator helps you rotate a point 90 degrees clockwise around the origin (0,0) in a 2D coordinate system. The origin is the center of rotation, and the transformation preserves distances from the origin.

How to Use This Calculator

To rotate a point 90 degrees clockwise about the origin:

Enter the original x-coordinate of the point in the "Original X" field.
Enter the original y-coordinate of the point in the "Original Y" field.
Click the "Calculate" button to see the rotated coordinates.
The result will show the new coordinates after rotation.

The calculator uses the standard rotation matrix for 90-degree clockwise rotation about the origin.

The Rotation Formula

When rotating a point (x, y) 90 degrees clockwise about the origin, the new coordinates (x', y') are calculated using the following transformation:

x' = y y' = -x

This formula swaps the x and y coordinates and negates the new x coordinate. The origin (0,0) remains unchanged.

Note: This is a 90-degree clockwise rotation. For counter-clockwise rotation, the formula would be x' = -y and y' = x.

Worked Example

Let's rotate the point (3, 4) 90 degrees clockwise about the origin.

Original point: (3, 4)

After rotation:

x' = y = 4

y' = -x = -3

Rotated point: (4, -3)

You can verify this by plotting the points on graph paper or using the calculator above.

Frequently Asked Questions

What does it mean to rotate about the origin?: Rotating about the origin means using the point (0,0) as the center of rotation. All points rotate around this fixed point.
Can I rotate points counter-clockwise with this calculator?: No, this calculator specifically performs 90-degree clockwise rotations. For counter-clockwise rotations, you would need a different formula.
What happens to the origin when rotated?: The origin (0,0) remains unchanged because it is the center of rotation. All other points rotate around it.
Is this formula used in computer graphics?: Yes, this rotation matrix is commonly used in computer graphics and game development for 2D transformations.
Can I rotate multiple points at once?: This calculator handles one point at a time. For multiple points, you would need to use the formula for each point individually.