Do You Draw a Circle Clockwise or Counterclockwise

Performing Geometry Rotations: Your Complete Guide

The post-obit pace-by-stride guide will testify yous how to perform geometry rotations of figures 90, 180, 270, and 360 degrees clockwise and counterclockwise and the definition of geometry rotations in math! (Free PDF Lesson Guide Included!)

Welcome to this free lesson guide that accompanies this Geometry Rotations Explained Video Tutorial where you volition larn the answers to the following cardinal questions and information:

What is the geometry rotation definition and what is the definition of rotation in math?
How to perform clockwise and counterclockwise rotations
How tin y'all rotate a triangle near the origin
Several geometry rotation examples

This Complete Guide to Geometry Rotations includes several examples, a step-past-step tutorial, a PDF lesson guide, and an animated video tutorial.

Rotation Geometry Definition

Earlier you learn how to perform rotations, let's speedily review the definition of rotations in math terms.

Rotation Geometry Definition: A rotation is a change in orientation based on the post-obit possible rotations:

xc degrees clockwise rotation
90 degrees counterclockwise rotation
180 degree rotation
270 degrees clockwise rotation
270 degrees counterclockwise rotation
360 caste rotation

Annotation that a geometry rotation does not result in a change or size and is non the same as a reflection!

Clockwise vs. Counterclockwise Rotations

There are 2 different directions of rotations, clockwise and counterclockwise:

Clockwise Rotations (CW) follow the path of the hands of a clock. These rotations are denoted by negative numbers.

Counterclockwise Rotations (CCW) follow the path in the contrary direction of the easily of a clock. These rotations are denoted by positive numbers.

Clockwise rotations are denoted by negative numbers.

Counterclockwise rotations are denoted by positive numbers.

Note that the management of rotation (CW or CCW) doesn't thing for 180 and 360-caste rotations, since they will both bring you to the same spot (more than on this after).

Geometry Rotation Notation

Note that the following note is used to show what kind of rotation is being performed.

For example, Figure i is a rotation of -270 degrees (which is a CW rotation).

Now you lot are fix to try a few geometry dilation examples!

Geometry Counterclockwise Rotation Examples

Instance 01: ninety Degrees Counterclockwise About the Origin

Since 90 is positive, this will be a counterclockwise rotation. — Since 90 is positive, this volition be a counterclockwise rotation.

In this example, y'all have to rotate Point C positive 90 degrees, which is a i quarter turn counterclockwise.

Bespeak C lays in the 1st quadrant.

To perform the ninety-caste counterclockwise rotation, imagine rotating the unabridged quadrant ane-quarter turn in a counterclockwise direction.

Note the location of Point C', the prototype of Betoken C later a 90-degree rotation.

And this process could be repeated if y'all wanted to rotation Bespeak C 180 degrees or 270 degrees counterclockwise:

Point C after a 180-degree rotation. — Indicate C after a 180-caste rotation.

This example should help you lot to visually sympathize the concept of counterclockwise geometry rotations. Side by side, y'all will learn the rules for performing counterclockwise rotations.

>>> Before y'all move on, have some time to visualize what rotations await like on the coordinate aeroplane.

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Counterclockwise Rotation Rules

Y'all can use the post-obit rules when performing any counterclockwise rotation.

By applying these rules to Indicate C (3,6) in the last instance (Figure 2), you can see how applying the dominion creates points that correspond with the graph!

Left: replace x with 3. Right: replace x with -9

These points should look familiar! They are the points that you plotted in the concluding example!

Geometry Clockwise Rotation Examples

Case 01: 90 Degrees Clockwise About the Origin

Since the rotation is 90 degrees, yous will rotating the point in a clockwise direction.

Now imagine rotating the entire quaternary quadrant i-quarter turn in a clockwise management:

Note the location of Point D', the epitome of Bespeak D after a -90-degree rotation.

And this procedure could be repeated if you wanted to rotation Indicate D -180 degrees or -270 degrees counterclockwise:

Point D after -180 rotation — Signal D after -180 rotation

Point D after -270 rotation — Indicate D subsequently -270 rotation

This example should help yous to visually sympathize the concept of clockwise geometry rotations. Side by side, y'all volition learn the rules for performing clockwise rotations.

>>> Before yous move on, accept some fourth dimension to visualize what rotations look like on the coordinate plane.

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Clockwise Rotation Rules

You lot tin can use the following rules when performing any clockwise rotation.

By applying these rules to Point D (5,-eight) in the last instance (Effigy 3), y'all can run into how applying the rule creates points that correspond with the graph!