Transformation_of_matrices

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Transformation of Matrices : 

Transformation of Matrices Applying the Operations of Matrices

Definitions : 

Definitions Let’s define some terms … Another way to think about a translation is to imagine a shape sliding across a page to a new location.

Examples : 

Examples Let’s take a look at an example of how this works. You will need to use graph paper to accomplish the tasks in this section More definitions: A PRE-IMAGE is the graph of a shape BEFORE it is transformed. The IMAGE is the graph of the shape AFTER it is transformed.

Examples … continued : 

Examples … continued Let’s write the coordinates of the vertices in a matrix. Notice how the x-coordinates appear on the top row and the y-coordinates appear on the bottom row. By the way – it the order in which you write the coordinates is not important. Since we are asked to translate the pre-image 6 units to the right (X – direction) and 4 units down (y- direction) … we can write a translation matrix!

Example - continued : 

Example - continued Now we can add the matrix containing the coordinates of the pre-image to the translation matrix and generate the matrix containing the coordinates of the new image. Here is the picture of the translation

Reflections & Rotations : 

Reflections & Rotations We can use matrix multiplication to reflect a figure over the x-axis or the y-axis Rotate a figure either 90°, 180°, or 270° about the origin. All you need to know is which matrix to use…

Examples : 

Examples Here is an example Please notice that you always put the transformation matrix in FRONT of the matrix with the vertices.

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