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Rotate 90 Degrees Counterclockwise Calculator

Reviewed by Calculator Editorial Team

This calculator helps you rotate a point or shape 90 degrees counterclockwise around the origin (0,0). Whether you're working with coordinates in a 2D plane or transforming shapes in computer graphics, this tool provides an accurate and efficient solution.

How to Use This Calculator

Using the rotate 90 degrees counterclockwise calculator is straightforward. Follow these steps:

  1. Enter the original coordinates of the point you want to rotate in the X and Y input fields.
  2. Click the "Calculate" button to perform the rotation.
  3. View the rotated coordinates in the result section.
  4. Use the "Reset" button to clear the inputs and start over.

The calculator will display the new coordinates after the rotation, along with a visualization of the transformation.

Formula Explained

Rotating a point 90 degrees counterclockwise around the origin involves a simple transformation of the original coordinates. The formula for this rotation is:

Rotation Formula

For a point (x, y), the rotated coordinates (x', y') after a 90° counterclockwise rotation are:

x' = -y

y' = x

This formula effectively swaps the x and y coordinates and negates the new x coordinate, resulting in a 90-degree counterclockwise rotation.

Worked Examples

Let's look at a couple of examples to see how the rotation works in practice.

Example 1: Rotating Point (3, 4)

Original coordinates: (3, 4)

After 90° counterclockwise rotation:

x' = -4 = -4

y' = 3 = 3

Rotated coordinates: (-4, 3)

Example 2: Rotating Point (-2, 5)

Original coordinates: (-2, 5)

After 90° counterclockwise rotation:

x' = -5 = -5

y' = -2 = -2

Rotated coordinates: (-5, -2)

These examples demonstrate how the rotation formula works for different coordinate pairs.

Frequently Asked Questions

What is a 90-degree counterclockwise rotation?

A 90-degree counterclockwise rotation is a transformation that turns a point or shape to the left by 90 degrees around the origin (0,0).

How do I rotate a point 90 degrees counterclockwise?

To rotate a point 90 degrees counterclockwise, you can use the formula x' = -y and y' = x, where (x, y) are the original coordinates.

Can I rotate a shape 90 degrees counterclockwise?

Yes, you can rotate an entire shape by applying the 90-degree counterclockwise rotation to each of its vertices.

What happens if I rotate a point 90 degrees counterclockwise multiple times?

Rotating a point 90 degrees counterclockwise four times will return it to its original position, as four 90-degree rotations complete a full 360-degree turn.