The clockwise rotation of \(90^\) counterclockwise. Take note of the direction of the rotation, as it makes a huge impact on the position of the image after rotation. The angle of rotation should be specifically taken. 'Rotation' means turning around a center: The distance from the center to any point on the shape stays the same.
![formulas of rotations geometry rules formulas of rotations geometry rules](https://1.bp.blogspot.com/-_lR7YIXM4kU/YFiuqoxwYGI/AAAAAAAAH_Y/nFg2BRJYdEEH5T2wUzP3d73x8X5P9tBUACLcBGAsYHQ/s16000/Example%2B6%2Brotation%2Bof%2Bpoints%2Bby%2Busing%2Bformula.png)
Generally, the center point for rotation is considered \((0,0)\) unless another fixed point is stated. The following basic rules are followed by any preimage when rotating:
![formulas of rotations geometry rules formulas of rotations geometry rules](https://showme0-9071.kxcdn.com/files/116644/pictures/thumbs/2092781/last_thumb1441246573.jpg)
Solution: Using the rotation formula, After rotation of 90 (CCW), coordinates of the point (x, y) becomes: (-y, x) Hence the point K (5, 7) will have the new position at (-7, 5) Answer: Therefore, the coordinates of the image are (-7, 5). There are some basic rotation rules in geometry that need to be followed when rotating an image. Example 1: Find the position of the point K (5, 7) after the rotation of 90 (CCW) using the rotation formula. In other words, the needle rotates around the clock about this point. In the clock, the point where the needle is fixed in the middle does not move at all. In all cases of rotation, there will be a center point that is not affected by the transformation. Examples of rotations include the minute needle of a clock, merry-go-round, and so on.
![formulas of rotations geometry rules formulas of rotations geometry rules](https://images.squarespace-cdn.com/content/v1/54905286e4b050812345644c/1588267186695-7PKJUVC9E53Q5J84ONDM/ke17ZwdGBToddI8pDm48kC8DNHesNOYP21dkifzZcEZZw-zPPgdn4jUwVcJE1ZvWQUxwkmyExglNqGp0IvTJZamWLI2zvYWH8K3-s_4yszcp2ryTI0HqTOaaUohrI8PID9HG-FSGNUSlv2KpHTKOnMNGqDIj5Hd83sIDBRNvsc8/Snip20200430_32.png)
Rotations are transformations where the object is rotated through some angles from a fixed point. So, we know that rotation is a movement of an object around a center.īut what about when dealing with any graphical point or any geometrical object? How are we supposed to rotate these objects and find their image? In this section, we will understand the concept of rotation in the form of transformation and take a look at how to rotate any image. We experience the change in days and nights due to this rotation motion of the earth. Whenever we think about rotations, we always imagine an object moving in a circular form.