90 Degrees Clockwise Rotation Calculator

This calculator helps you determine the new coordinates of a point after rotating it 90 degrees clockwise around another reference point. This is useful in geometry, computer graphics, and engineering applications where precise point transformations are needed.

How to Use This Calculator

To use the 90-degree clockwise rotation calculator:

Enter the original coordinates of the point you want to rotate in the "Original X" and "Original Y" fields.
Enter the coordinates of the point around which you want to rotate in the "Center X" and "Center Y" fields.
Click the "Calculate" button to see the new coordinates after rotation.
The result will show the new X and Y coordinates of the rotated point.

You can also reset the form to start over with new values by clicking the "Reset" button.

Formula Explained

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

Rotation Formulas

New X = a + (y - b)

New Y = b - (x - a)

Where:

(x, y) are the original coordinates of the point to be rotated
(a, b) are the coordinates of the center of rotation
(New X, New Y) are the coordinates after rotation

These formulas work by translating the coordinate system so that the center of rotation becomes the origin, performing the rotation, and then translating back to the original coordinate system.

Worked Examples

Example 1: Rotating a Point Around the Origin

Let's rotate the point (3, 4) 90 degrees clockwise around the origin (0, 0).

Using the formulas:

Calculation

New X = 0 + (4 - 0) = 4

New Y = 0 - (3 - 0) = -3

The rotated point is at (4, -3).

Example 2: Rotating a Point Around Another Point

Now let's rotate the point (5, 7) 90 degrees clockwise around the point (2, 3).

Using the formulas:

Calculation

New X = 2 + (7 - 3) = 6

New Y = 3 - (5 - 2) = 0

The rotated point is at (6, 0).

Frequently Asked Questions

What is a 90-degree clockwise rotation?: A 90-degree clockwise rotation is a transformation that moves every point of an object or coordinate system in a circular path around a fixed point, in the direction of a clock's hands, by 90 degrees.
How do I rotate a point around another point?: To rotate a point around another point, you first translate the coordinate system so that the rotation center becomes the origin, then apply the rotation matrix, and finally translate back to the original coordinate system.
Can I rotate multiple points at once?: This calculator works with one point at a time. For multiple points, you would need to apply the rotation to each point individually.
What if I want to rotate counterclockwise?: The formulas provided rotate clockwise. For counterclockwise rotation, you would use the negative of these formulas or use a different set of transformation equations.