Rotation Formula

About Rotation Formula

The rotation formula informs us how a point rotates in relation to the origin. To get the position of the point after rotation, apply the rotation formula. A circular motion around a certain axis of rotation or point of rotation is known as rotation. Rotation can be performed in two primary directions: clockwise and anti-clockwise or counter-clockwise. Check out the list of Maths formulas prepared by the experts of Home tution.com

What Is Rotation Formula?

After a specific rotation to a finite degree of rotation, the rotation formula will give us the exact location of a point. The type of rotation done to the point with regard to the origin determines the rotation formula. A geometric two-dimensional shape can be transformed in one of four different ways.

The following table shows the rotation formula based on the type of rotation performed

Rotation	Coordinates of the point	Coordinates of the Image of the point after Rotation
Rotation of 90°(CW)	(x, y)	(y, -x)
Rotation of 90°(CCW)	(x, y)	(-y, x)
Rotation of 180°	(x, y)	(-x, -y)
Rotation of 270°(CW)	(x, y)	(-y, x)
Rotation of 270°(CCW)	(x, y)	(y, -x)

Rotation of 90°(CW)	(x, y)(y,-x)
Rotation of 90°(CCW)	(x, y)(y,-x)
Rotation of 180°	(x, y)(-x,-y)
Rotation of 270°(CW)	(x, y)(-y,x)
Rotation of 270°(CCW)	(x, y)(y,-x)