Rotation 90 Degrees Counterclockwise About The Origin Calculator

This calculator helps you rotate a point 90 degrees counterclockwise about the origin (0,0) in a 2D coordinate system. The result shows the new coordinates after rotation.

How to Use This Calculator

To rotate a point 90 degrees counterclockwise about the origin:

Enter the original x-coordinate of the point in the first input field.
Enter the original y-coordinate of the point in the second input 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 counterclockwise rotation about the origin.

Rotation Formula

For a point (x, y) rotated 90 degrees counterclockwise about the origin, the new coordinates (x', y') are calculated using the following formulas:

Rotation Formulas

x' = -y

y' = x

This transformation swaps the coordinates and changes the sign of the new x-coordinate.

Worked Example

Let's rotate the point (3, 5) 90 degrees counterclockwise about the origin.

Original coordinates: x = 3, y = 5
Apply the rotation formulas:
- x' = -y = -5
- y' = x = 3
Rotated coordinates: (-5, 3)

The point (3, 5) moves to (-5, 3) after the rotation.

Frequently Asked Questions

What does rotating a point 90 degrees counterclockwise about the origin do?: It swaps the x and y coordinates and changes the sign of the new x-coordinate, effectively moving the point to a perpendicular position in the counterclockwise direction.
Can I rotate a point 90 degrees clockwise about the origin?: Yes, the formulas for 90-degree clockwise rotation are x' = y and y' = -x. You can use the same calculator by swapping the formulas.
What happens if I rotate the origin point (0,0)?: The origin remains at (0,0) because rotating it doesn't change its position.
Is this rotation the same for all points in the plane?: Yes, the 90-degree counterclockwise rotation about the origin is the same for all points in the 2D plane.