1. What is a 90 Degree Triangle Rotation?

Definition: This calculator rotates a triangle defined by three points 90 degrees clockwise around the origin (0,0).

Purpose: It helps in computer graphics, engineering, and mathematics to transform shapes while preserving their properties.

2. How Does the Rotation Work?

The calculator uses the rotation formula:

Explanation: Each point of the triangle is transformed by swapping the x and y coordinates and negating the new x value.

3. Importance of Rotation Calculations

Details: Rotations are fundamental in computer graphics, robotics, and physics simulations. They preserve distances and angles between points.

4. Using the Calculator

Tips: Enter the (x,y) coordinates for all three points of your triangle. The calculator will show their positions after a 90° clockwise rotation.

5. Frequently Asked Questions (FAQ)

Q1: What if I want counter-clockwise rotation?
A: The formula would be (x,y) → (-y,x). You can modify the calculation accordingly.

Q2: Can I rotate around a different point?
A: First translate the triangle so your rotation point is at the origin, rotate, then translate back.

Q3: Does this preserve the triangle's area?
A: Yes, rotation is a rigid transformation that preserves all lengths and angles.

Q4: How do I rotate other angles?
A: For θ degrees, use: x' = x·cosθ - y·sinθ, y' = x·sinθ + y·cosθ

Q5: Can I rotate polygons with more sides?
A: Yes, the same formula applies to each vertex of any polygon.