The 90 Degrees Counterclockwise Calculator is a tool used in geometry to rotate a point by 90 degrees counterclockwise around the origin (0, 0). This rotation involves changing the coordinates of a point (x, y) to a new position based on a specific mathematical formula.
Formula of 90 Degrees Counterclockwise Calculator
If you have a point (x, y) that you want to rotate 90 degrees counterclockwise about the origin (0, 0), you can use the following formula:
New_x = -y
New_y = x
Here’s how it works:
- The new x-coordinate (New_x) is obtained by taking the negative of the original y-coordinate (y).
- The new y-coordinate (New_y) is obtained by taking the original x-coordinate (x). This formula effectively swaps the x and y coordinates and changes the sign of the new x-coordinate, resulting in a 90-degree counterclockwise rotation about the origin.
Table of General Terms
| Original Point (x, y) | Rotated Point (New_x, New_y) |
|---|---|
| (1, 1) | (-1, 1) |
| (2, 3) | (-3, 2) |
| … | … |
This table provides pre-calculated examples of the rotated points for common coordinate pairs, aiding users without the need for manual calculation each time.
Example of 90 Degrees Counterclockwise Calculator
Let’s consider a point (3, 4). Applying the formula: New_x = -4 = -(-4) = 4 New_y = 3 Hence, the rotated point becomes (4, 3).
Most Common FAQs
A: 90 degrees counterclockwise rotation is often employ in computer graphics, transformations in geometry, and various mathematical applications.
A: Yes, the formula applies to any point in a two-dimensional coordinate system, allowing the calculation of the rotated point.
A: This tool finds extensive use in various fields, such as computer graphics, image processing, game development, and mathematical modeling.