"Rotation transformation matrix" is the matrix which can be used to make rotation transformation of a figure.

Even though students can get this stuff on internet, they do not understand exactly what has been explained.

To
make the students to understand the stuff "Rotation transformation
using matrix", we have explained the different rules which we apply to
make rotation-transformation.

Rules on finding rotated image

90° rotation (clock wise)

90° rotation (counter clock wise)

180° rotation (clock wise and counter clock wise)

Once
students understand the rules which they have to apply for rotation
transformation, they can easily make rotation transformation of a
figure.

Let us consider the following example to have better understanding of rotation transformation using matrices.

Question :

Let A ( -2, 1), B (2, 4) and (4, 2)
be the three vertices of a triangle. If this triangle is rotated about 90° counter clockwise, find the vertices of the rotated image A'B'C' using matrices.

Solution:

Step 1 :

First we have to write the vertices of the given triangle ABC in matrix form as given below.

Step 2 :

Since
the triangle ABC is rotated about 90° counter clockwise, to get the rotated image,
we have to multiply the above matrix by the matrix given below.

Step 3 :

Now, let us multiply the two matrices.

Step 4 :

Now we can get vertices of the rotated image A'B'C' from the resultant matrix.

Vertices of the reflected image are

A' (-1 , -2) , B' (-4 , 2) and C' (-2 , 4)

After having gone through the
example given above, we hope that the students would have understood the
way in which they have to find the vertices of the rotated image
using matrices.

How to sketch the rotated figure?

1. First we have to plot the vertices of the pre-image.

2. In the above problem, the vertices of the pre-image are

A ( -2, 1 ) , B ( 2, 4 ) and C ( 4 , 2 )

3. When we plot these points on a graph paper, we will get the figure of the pre-image (original figure).

4. When we rotate the given figure about 90° counter clock wise, vertices of the image are

A' (-1 , -2) , B' (-4 , 2) and C' (-2 , 4)

7. When plot these points on the graph paper, we will get the figure of the image (rotated figure).