Rotate 90 Degrees About The Origin Calculator

Rotating a point 90 degrees about the origin is a fundamental transformation in coordinate geometry. This calculator provides an easy way to perform this operation and understand the underlying mathematics.

How to Use This Calculator

To rotate a point 90 degrees 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.
Select the direction of rotation (clockwise or counter-clockwise).
Click the "Calculate" button to see the rotated coordinates.

The calculator will display the new coordinates after rotation and show a visualization of the transformation.

The Rotation Formula

Rotating a point (x, y) 90 degrees about the origin can be done using a simple transformation matrix. The formulas for clockwise and counter-clockwise rotation are:

Counter-clockwise rotation:

x' = -y

y' = x

Clockwise rotation:

x' = y

y' = -x

Where (x', y') are the coordinates after rotation.

Worked Examples

Example 1: Counter-clockwise rotation

Original point: (3, 4)

After counter-clockwise rotation:

x' = -4

y' = 3

New coordinates: (-4, 3)

Example 2: Clockwise rotation

Original point: (5, -2)

After clockwise rotation:

x' = -2

y' = -5

New coordinates: (-2, -5)

These examples demonstrate how the coordinates change when rotating points about the origin.

Frequently Asked Questions

What is the difference between clockwise and counter-clockwise rotation?

Clockwise rotation moves points in the direction of a clock's hands, while counter-clockwise rotation moves points in the opposite direction. The formulas for each are different as shown above.

Can I rotate points by other angles besides 90 degrees?

Yes, but this calculator specifically handles 90-degree rotations. For other angles, you would need a different calculator or formula.

What happens if I rotate the origin point itself?

The origin (0, 0) remains unchanged regardless of the rotation direction, as it's the center of rotation.

Is there a way to rotate multiple points at once?

This calculator handles one point at a time. For multiple points, you would need to perform the calculation for each point individually.