The Rotating Points Calculator is a versatile tool used to determine the new coordinates of a point after it has been rotated by a specified angle around either the origin or an arbitrary pivot point. This calculator simplifies complex mathematical calculations, making it easier to visualize and manipulate points in two-dimensional space.
Formula of Rotating Points Calculator
Rotation Around the Origin: When rotating a point (x, y) by an angle Θ counter-clockwise around the origin, the new coordinates are calculated using the following formulas:
New X coordinate: xf = x cos(Θ) - y sin(Θ)
New Y coordinate: yf = x sin(Θ) + y cos(Θ)
Rotation Around an Arbitrary Point: For rotating a point (xi, yi) by an angle Θ around a pivot point (xo, yo), the formulas are slightly modified as follows:
New X coordinate: xf = xo + (xi - xo) cos(Θ) - (yi - yo) sin(Θ)
New Y coordinate: yf = yo + (xi - xo) sin(Θ) + (yi - yo) cos(Θ)
General Terms Table:
| Rotation | Degrees | New X Coordinate | New Y Coordinate |
|---|---|---|---|
| 90° Counter-Clockwise (Around Origin) | 90 | -y | x |
| 180° (Around Origin) | 180 | -x | -y |
| 270° Counter-Clockwise (Around Origin) | 270 | y | -x |
Note: This table only shows rotations around the origin for simplicity. You can use the general formulas for rotations around any point.
Example of Rotating Points Calculator
Let’s consider a point with coordinates (2, 3) being rotate by 45 degrees counter-clockwise around the origin. Using the Rotating Points Calculator, we can determine the new coordinates as follows:
New X coordinate: xf = 2 * cos(45°) - 3 * sin(45°) ≈ -0.71 New Y coordinate: yf = 2 * sin(45°) + 3 * cos(45°) ≈ 3.54
Most Common FAQs:
The calculator simplifies the process of determining new coordinates after rotation, saving time and effort in mathematical calculations.
Simply input the initial coordinates of the point, the rotation angle, and optionally the pivot point coordinates, then click ‘Calculate’ to obtain the new coordinates.
No, the calculator is specifically design for two-dimensional rotations in a plane.
