Rotation rule for 90° clockwise
The rotation rule for 90° clockwise refers to the transformation of a point or object by rotating it 90 degrees in the clockwise direction around a fixed point
The rotation rule for 90° clockwise refers to the transformation of a point or object by rotating it 90 degrees in the clockwise direction around a fixed point. This rule can be applied in both two-dimensional and three-dimensional space.
In the two-dimensional case, to rotate a point (x, y) 90° clockwise about the origin, you can use the following formulas:
x’ = y
y’ = -x
Here, (x’, y’) represents the coordinates of the rotated point.
To understand the rotation rule visually, imagine a Cartesian coordinate system. When you rotate a point 90° clockwise, it moves from its original position to a new position with the same distance from the origin but in a different direction.
For example, let’s take the point (3, 4). Applying the rotation rule, we get:
x’ = 4
y’ = -3
So the rotated point will be (4, -3).
In three-dimensional space, the rotation rule for 90° clockwise can be applied similarly. It involves rotating the object around an axis, typically the z-axis. The formulas for rotating a point (x, y, z) 90° clockwise in three-dimensional space are as follows:
x’ = y
y’ = -x
z’ = z
Again, (x’, y’, z’) represents the coordinates of the rotated point.
The rotation rule for 90° clockwise is a fundamental concept in mathematics and has various applications in geometry, computer graphics, and physics. It helps in understanding and manipulating the positions and orientations of objects in space.
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