Rules of Rotations in Geometry: A Simplified Guide

Rotating points in geometry can seem daunting, but with a few simple rules, it becomes easy to master. One of the most important rules is that when rotating by 90 degrees, you swap the X and Y coordinates and make Y negative.

Let's take an example to illustrate this rule. Suppose we have a point (-2, -1) and want to rotate it 90 degrees. To do this, we would simply swap the X and Y coordinates, making Y negative, resulting in (1, -2). If we then rotate the point another 90 degrees, we will end up back where we started.

But what about rotating by 90 degrees again? The same rule applies: we swap the X and Y coordinates and make Y negative. This time, our point (-1, 2) becomes (-2, -1). Notice that when we rotate a point, its position changes, but it remains within the same quadrants.

So, to summarize, rotating by 90 degrees involves swapping the X and Y coordinates and making Y negative. When you have a point on (x, y), swap them and make y negative (-y, x) to perform a 90-degree rotation.

For those who prefer an algebraic approach, here is how it works: when you rotate by 90 degrees, you take your original X and Y coordinates and swap them. Then, make Y negative. Using this method, if we have a point (2, 1), rotating it by 90 degrees will result in (-1, 2).

By following these simple rules, you can master the art of rotating points in geometry and solve problems with ease.

Rules of rotations geometry