Rotation 90 Degrees Clockwise Calculator

Rotating a point or shape 90 degrees clockwise is a common transformation in geometry and computer graphics. This calculator provides an easy way to compute the new coordinates after a 90-degree clockwise rotation around the origin.

How to Use This Calculator

To use the rotation calculator:

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 to compute the new coordinates.
The result will show the new x and y coordinates after a 90-degree clockwise rotation.
Use the "Reset" button to clear all inputs and results.

The calculator also provides a visualization of the original and rotated points on a coordinate plane.

Formula Explained

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

New X = y

New Y = -x

This formula works because a 90-degree clockwise rotation swaps the x and y coordinates and changes the sign of the new y-coordinate.

For example, rotating the point (3, 4) 90 degrees clockwise would result in the point (4, -3).

Worked Examples

Example 1: Rotating a Point

Let's rotate the point (2, 5) 90 degrees clockwise.

Using the formula:

New X = 5

New Y = -2

The rotated point is (5, -2).

Example 2: Rotating a Shape

Consider a square with vertices at (1, 1), (1, -1), (-1, -1), and (-1, 1).

After a 90-degree clockwise rotation, the new vertices will be:

(1, 1) → (1, -1)
(1, -1) → (-1, -1)
(-1, -1) → (-1, 1)
(-1, 1) → (1, 1)

The square will appear to have rotated clockwise by 90 degrees.

Frequently Asked Questions

What is a 90-degree clockwise rotation?

A 90-degree clockwise rotation is a transformation that turns a point or shape to the right by 90 degrees around the origin (0,0).

How do I rotate a point 90 degrees clockwise?

To rotate a point (x, y) 90 degrees clockwise, swap the x and y coordinates and change the sign of the new y-coordinate. The new coordinates will be (y, -x).

What happens if I rotate a point 90 degrees clockwise multiple times?

Rotating a point 90 degrees clockwise four times will return it to its original position. Each rotation is equivalent to a 90-degree turn to the right.

Can I rotate a shape other than a point?

Yes, you can rotate any shape by applying the 90-degree clockwise rotation to each of its vertices. The entire shape will appear to have rotated by 90 degrees.