Matrix Transformations

1
Matrix Transformations
2
Transformations

• 2 2 matrices can be used to describe
  transformations in a 2-d plane.
• Before we look at this we are going to look at
  particular transformations in the 2D plane.
• A transformation is a rule which moves points
  about on a plane.
• Every transformation can be described as a
  multiple of x plus a multiple of y.

3
Transformations

• Lets look at a point A(-2,3) and map it to the
  co-ordinate (2x3y,3x-y)
• This gives us the co-ordinate
• (2-2 33, 3-23)
• (5,-9)
• Where would the co-ordinate (2,1)
  map to?

(-2,3)
(7,5)
(2,1)
(5,-9)
4
Transformations
x 2x 3y
y 3x - y
We could write this as x 2x 3y y 3x - y
x
y
x
y
5
Transformations
Writing it in matrix form is useful as we can now
multiply the object by our transformation matrix.
6
Transformations
Transform the rectangle below by the following
matrix.
Can you describe the transformation in words?
7
Transformations match

• Write down a matrix that represents the object
  triangle.
• Try multiplying the object triangle by the
  different transformations matrices.
• Match the image to the graphs and the
  descriptions.