Geometry transformations

This course is a part of Mathematics I, a 16-course Topic series from Khan Academy.

In this topic you will learn about the most useful math concept for creating video game graphics: geometric transformations, specifically translations, rotations, reflections, and dilations. You will learn how to perform the transformations, and how to map one figure into another using these transformations.

This course contains 8 segments:

Introduction to rigid transformations

The three rigid transformations are translations, rotations, and reflections. Get to know them and gain some experience in performing them on different figures.

Translations

Learn how to find the translation that maps a given figure to another, and how to manually draw the image of a translation.

Rotations

Learn how to find the rotation that maps a given figure to another, and how to manually draw the image of a rotation.

Reflections

Learn how to find the reflection that maps a given figure to another, and how to manually draw the image of a reflection.

Rigid transformations overview

After studying each rigid transformation in separate, it's time to take a broader look at those transformations: which properties are preserved under which kind of transformation, and how do we map shapes using sequences of rigid transformations?

Dilations

In addition to the three rigid transformation, there are the dilations, which expand or shrink figures while keeping the same proportions. These are extremely important in the subject of Similarity! Gain experience by performing dilation, learn how to find the dilation that maps a given figure to another, and learn how to manually draw the image of a dilation.

Properties & definitions of transformations

Let's continue our deep voyage through the world of transformations! Use your knowledge about the precise descriptions of the rigid transformations and their properties in various situations.

Symmetry

Learn about different kinds of symmetries of two-dimensional shapes, and analyze various shapes according to their symmetries.