Rotate Point 90 Degrees Counterclockwise Calculator
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Reviewed by Calculator Editorial Team
Rotating a point 90 degrees counterclockwise is a common operation in geometry and computer graphics. This calculator provides an easy way to perform the transformation and understand the underlying mathematics.
How to Use This Calculator
To rotate a point 90 degrees counterclockwise:
- 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
- Click the "Calculate" button
- View the rotated coordinates in the result section
- Optionally, view the visualization of the rotation
The calculator will show you the new coordinates after the rotation and provide a visual representation of the transformation.
The Rotation Formula
To rotate a point (x, y) 90 degrees counterclockwise around the origin (0, 0), you can use the following transformation:
Rotation Formula
New X = -y
New Y = x
This formula works because a 90-degree counterclockwise rotation swaps the x and y coordinates and changes the sign of the new x-coordinate.
Important Notes
- The rotation is performed around the origin (0, 0)
- Coordinates must be in Cartesian (x, y) format
- For rotations around other points, you would need to translate the point first
Worked Examples
Example 1: Simple Rotation
Original point: (3, 5)
After 90° counterclockwise rotation:
New X = -5
New Y = 3
Result: (-5, 3)
Example 2: Negative Coordinates
Original point: (-2, 4)
After 90° counterclockwise rotation:
New X = -4
New Y = -2
Result: (-4, -2)
These examples demonstrate how the rotation formula works with different coordinate values.
Visualizing the Rotation
The chart below shows the original point and its rotated position. The blue dot represents the original point, and the green dot shows the point after rotation.
The visualization helps you understand the geometric transformation that occurs when rotating a point 90 degrees counterclockwise.
FAQ
- What does rotating a point 90 degrees counterclockwise do?
- It transforms the point's coordinates by swapping the x and y values and changing the sign of the new x-coordinate.
- Can I rotate a point around a different center?
- Yes, but you would need to translate the point to the origin first, perform the rotation, and then translate it back.
- What's the difference between counterclockwise and clockwise rotation?
- Counterclockwise rotation moves points to the left, while clockwise rotation moves them to the right. The formulas are similar but with sign changes.
- Is this formula used in computer graphics?
- Yes, it's a fundamental operation in 2D graphics transformations, often used for sprite rotation and coordinate system conversions.