Rotate Triangle 90 Degrees Counterclockwise About The Origin Calculator

How to Use This Calculator

To rotate a triangle 90 degrees counterclockwise about the origin:

1. Enter the coordinates of the three vertices of your triangle in the input fields.
2. Click "Calculate" to perform the rotation.
3. View the rotated coordinates in the result panel.
4. Use the visualization to see the transformation.

The calculator will show you the new coordinates after rotation and display a before-and-after chart.

The Math Behind Rotation

Rotating a point (x, y) 90 degrees counterclockwise about the origin transforms it to (-y, x). This is derived from the standard 2D rotation matrix:

This transformation preserves the distance from the origin but changes the angle by 90 degrees. The same formula applies to all three vertices of the triangle.

Worked Example

Let's rotate a triangle with vertices at (1, 2), (3, 4), and (5, 6) 90 degrees counterclockwise about the origin.

1. First vertex (1, 2) becomes (-2, 1)
2. Second vertex (3, 4) becomes (-4, 3)
3. Third vertex (5, 6) becomes (-6, 5)

The original triangle is now rotated 90 degrees counterclockwise, with all points moved to new positions while maintaining their relative positions to each other.