Rotation Formula
We know that rotation can be done in both clockwise and anti-clockwise directions. In mathematics, rotation refers to the circular motion of a figure around a fixed point, particularly the origin. This leads to a change in the coordinates of the point or figure that is rotated. The rotation can be done around any angle. Let us have a look at the rotation formula for some common angles in both directions when the figure is rotated around the origin.
Angle and Direction of Rotation | Initial Coordinates of the Point | Coordinates of the Point after Rotation |
---|---|---|
90° clockwise | (x, y) | (y, -x) |
90° anti-clockwise | (x, y) | (-y, x) |
180° both clockwise and anti-clockwise | (x, y) | (-x, -y) |
270° clockwise | (x, y) | (-y, x) |
270° anti-clockwise | (x, y) | (y, -x) |
There is also a general rotation formula when the rotation is not around the origin but around a point Q(α, β) which is as follows:
Let the initial coordinates of the point be (x, y). Then the coordinates of the point after rotation (x’, y’) around point Q are given using
(x’, y’) = {α + (x-α)cosθ – (y-β)sinθ, β + (x-α)sinθ – (y-β)cosθ}
Rotation
In real life, we know that the Earth rotates on its own axis and the moon also rotates on its axis. But what basically rotation is? Also, geometry deals with four basic types of transformations that are Rotation, Reflection, Translation, and Resizing. In this article, we shall read about the fundamental concept of rotation.
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