Rotate A Figure 90 Degrees Calculator

Rotating a figure 90 degrees is a fundamental geometric transformation that changes the orientation of a shape without altering its size or shape. This calculator helps you determine the new coordinates of points after a 90-degree rotation around a specified center point.

How to Use This Calculator

To rotate a figure 90 degrees using this calculator:

Enter the original coordinates of the point you want to rotate.
Specify the center of rotation (default is the origin (0,0)).
Choose the direction of rotation (clockwise or counter-clockwise).
Click "Calculate" to see the new coordinates after rotation.
Review the result and visualization to understand the transformation.

The calculator will display the new coordinates and provide a visual representation of the rotation.

Rotation Formula

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

For clockwise rotation: x' = a + (y - b) y' = b - (x - a) For counter-clockwise rotation: x' = a - (y - b) y' = b + (x - a)

Where:

(x, y) are the original coordinates
(a, b) is the center of rotation
(x', y') are the new coordinates after rotation

These formulas account for the rotation around any arbitrary center point, not just the origin.

Worked Example

Let's rotate the point (3, 5) 90 degrees clockwise around the center (1, 2).

Original point: (3, 5)
Center of rotation: (1, 2)
Direction: Clockwise

Using the clockwise rotation formula:

x' = 1 + (5 - 2) = 1 + 3 = 4 y' = 2 - (3 - 1) = 2 - 2 = 0

The new coordinates after rotation are (4, 0).

Note

The distance from the center remains the same, but the position relative to the center changes.

Visualization

The calculator includes an interactive chart that shows the original point, center of rotation, and the rotated point. This helps visualize the transformation.

Key features of the visualization:

Original point in blue
Center of rotation in red
Rotated point in green
Clear labeling of all points

FAQ

Can I rotate a figure 90 degrees around any point?: Yes, this calculator allows you to specify any center point for rotation. The formulas account for rotation around any arbitrary point.
What happens if I rotate a figure 90 degrees twice?: Rotating a figure 90 degrees twice (180 degrees total) will return it to its original orientation but mirrored across the center of rotation.
Is there a difference between clockwise and counter-clockwise rotation?: Yes, the direction of rotation affects the sign of the coordinates in the rotation formulas. Clockwise rotation uses positive values, while counter-clockwise uses negative values.
Can I rotate multiple points at once?: Currently, this calculator rotates one point at a time. For multiple points, you would need to perform the calculation for each point individually.
What if I want to rotate a figure 90 degrees in 3D space?: This calculator is designed for 2D rotation. For 3D rotation, you would need a different set of formulas and a more complex visualization.