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Rotate Triangle 90 Degrees Clockwise Calculator

Reviewed by Calculator Editorial Team

This calculator helps you rotate a triangle 90 degrees clockwise around a specified point. Whether you're working on geometry problems, game development, or CAD design, understanding how to rotate triangles is essential. The calculator provides the new coordinates of the triangle's vertices after rotation.

How to Use This Calculator

To rotate a triangle 90 degrees clockwise, follow these steps:

  1. Enter the coordinates of the triangle's vertices in the input fields.
  2. Specify the rotation point (default is the origin (0,0)).
  3. Click the "Calculate" button to see the rotated coordinates.
  4. Review the result and use the chart to visualize the rotation.

The calculator will display the new coordinates of the triangle's vertices after rotation. You can also reset the inputs to start over.

Rotation Formula

To rotate a point (x, y) 90 degrees clockwise around another point (a, b), use the following transformation:

New X-coordinate: x' = a + (y - b)

New Y-coordinate: y' = b - (x - a)

This formula works by translating the point to the origin, applying the rotation matrix for 90 degrees clockwise, and then translating back.

Worked Example

Let's rotate a triangle with vertices at (1, 2), (3, 4), and (5, 6) 90 degrees clockwise around the origin (0, 0).

Original Coordinates Rotated Coordinates
(1, 2) (2, -1)
(3, 4) (4, -3)
(5, 6) (6, -5)

As shown, each vertex's coordinates are transformed according to the rotation formula.

Frequently Asked Questions

How do I rotate a triangle 90 degrees counterclockwise?
To rotate counterclockwise, use the formulas: x' = a - (y - b) and y' = b + (x - a).
Can I rotate a triangle around any point?
Yes, the calculator allows you to specify any rotation point (a, b). The default is the origin (0, 0).
What if I enter non-numeric values?
The calculator will alert you to enter valid numbers for all coordinates.
How accurate are the results?
The results are calculated with JavaScript's floating-point precision, which is accurate for most practical purposes.