Examples of Transformations on a Graph

Hi, and welcome to this video lesson on rotation, translation, and reflection of objects on a plane. No, not that kind of plane. No, not that kind either. Like this. Here’s our object. I want to rotate it on this plane, which is like a graph or a background.

If you think of rotating this object like you would a tire, that might help. If I want to rotate this picture, that means just spinning it around its center, like this. An image can be rotated from 0 to 360 degrees, like a circle.

Reflection is just like what it sounds: Mirroring something. Take our image, and then decide which way we are going to reflect it. Perhaps to the left. Then, our reflection might look like this.

Usually in math, you are using a coordinate graph, so we might say the image is reflected across the y axis, which is this vertical line here. Translation is not translating words into different languages, so don’t worry.

No. Mathematical translation simply means to move something. To make it travel, like this. Translating this image to the right 2 spaces on the x axis (this is the horizontal line) simply means moving it to the right 2 spaces.

All the different ways that we’ve moved or changed this object are called transformations. Now I’m going to give you a few examples and I want you to try to figure out how I transformed this specific object.

Here’s an image. How has it been transformed? It’s been reflected across the y axis, or this vertical line here. See? Here’s another. How has it been transformed? Well, it’s been moved, or translated, to the left 4 spaces. I hope that helps. Thanks for watching this video lesson, and until next time: Happy study.