Formulas of Rotations in Geometry Rules

In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. One common type of transformation is rotation. When we rotate a point by a certain angle, its coordinates change accordingly. In this article, we will explore the formulas and rules for rotations in geometry.

180 Degree Rotation

When you rotate a point by 180 degrees, you take your original x and y values and make them negative. For example, if you have a point on (2, 1) and rotate it by 180 degrees, it will end up at (-2, -1).

90 Degree Rotation (CCW)

When you rotate a point by 90 degrees counterclockwise (CCW), you take your original x value and swap it with the y value. Then, make the y value negative. Using this formula, we can find the new position of a point after a rotation of 90 degrees.

For example, let's consider a point K on (5, 7). After rotating it by 90 degrees CCW using the rotation formula, the coordinates of the point become (-7, 5).

More Examples

Let's see what happens if we rotate our point K by another 90 degrees. Since we are rotating in the same direction (CCW), the result will be the same as before: (-7, 5). If we rotate it by -90 degrees, which is the same as rotating 90 degrees clockwise (CW), the result will be the same as well.

Rotating a Point by Multiple Angles

If you understand the rules for rotating by 180 and 90 degrees, then rotating by other angles should be no issue. For example, if we rotate our point K by another 90 degrees CCW, it will end up at (1, -2). If we continue to rotate it by 90 degrees in the same direction, we will eventually return to the original position.

In conclusion, rotation is a fundamental concept in geometry, and understanding the formulas and rules for rotations can help you solve problems more efficiently. Whether you are rotating by 180 or 90 degrees, the key is to understand how the coordinates of a point change when it is rotated by a certain angle.

Formulas of rotations geometry rules