Transforming shapes with matrices

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/1
?
Intros
Lessons
  1. Transforming shapes with matrices overview
0/6
?
Examples
Lessons
  1. Finding the Transformed Polygons
    Apply the transformation matrix TT to the following vertices to find the transformed vertices:
    1. Transforming shapes with matrices
    2. Transforming shapes with matrices
    3. Transforming shapes with matrices
  2. Graphing the Transformed Polygon
    Plot the vertices Transforming shapes with matrices on the graph. Then apply the transformation matrix Transforming shapes with matrices, to the vertices to find the transformed polygon, and then plot the transformed polygon on the graph.
    1. Plot the vertices Transforming shapes with matrices on the graph. Then apply the transformation matrix Transforming shapes with matrices, to the vertices to find the transformed polygon, and then plot the transformed polygon on the graph.
      1. Plot the vertices Transforming shapes with matrices on the graph. Then apply the transformation matrix Transforming shapes with matrices, to the vertices to find the transformed polygon, and then plot the transformed polygon on the graph.
        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 vertices of a square be vertices of a square and TT be a transformation matrix.
        Then we can transform the square by combining the vertices into a matrix (denoted by AA), and multiply it by the transformation matrix TT. In other words,
        vertices of a square in a matrix

        And TATA is the transformed square.
        Of course, this idea can also apply to other shapes other than squares.