# Transforming shapes with matrices

0/1

##### Intros

0/6

##### Examples

###### Lessons

**Finding the Transformed Polygons**

Apply the transformation matrix $T$ to the following vertices to find the transformed vertices:**Graphing the Transformed Polygon**

Plot the vertices on the graph. Then apply the transformation matrix , to the vertices to find the transformed polygon, and then plot the transformed polygon on the graph.- Plot the vertices on the graph. Then apply the transformation matrix , to the vertices to find the transformed polygon, and then plot the transformed polygon on the graph.
- Plot the vertices on the graph. Then apply the transformation matrix , to the vertices to find the transformed polygon, and then plot the transformed polygon on the graph.

###### Free to Join!

StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.

#### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.#### Make Use of Our Learning Aids

#### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.#### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Notes

In this section, we will learn how to transform shapes with matrices. Instead of one column vector, we are going to have multiple vertices which create a shape. What we can do to this shape is use the transformation matrix to change the length and size of that shape. To do this computation, we merge all the vertices into one matrix and then multiply it with the transformation matrix. Doing so will give us another matrix. We will then take a look at each transformed vertices separately in the matrix to see the new transformed shape. Note that transforming the shape does not change the number of sides. We will take a look at some questions which involve transforming shapes, and then graph them to notice the changes between the normal shape and the transformed shape.

Let be vertices of a square and $T$ be a transformation matrix.

Then we can transform the square by combining the vertices into a matrix (denoted by $A$), and multiply it by the transformation matrix $T$. In other words,

And $TA$ is the transformed square.

Of course, this idea can also apply to other shapes other than squares.

Then we can transform the square by combining the vertices into a matrix (denoted by $A$), and multiply it by the transformation matrix $T$. In other words,

And $TA$ is the transformed square.

Of course, this idea can also apply to other shapes other than squares.

2

videos

remaining today

remaining today

5

practice questions

remaining today

remaining today