TRANSFORMATIONS
USING MATRICES

About the topic "Transformations using matrices"

"Transformations using matrices" is the stuff which is much required for the students who study geometry in  both school level and college level math.

Very few websites on internet give this stuff to the students. 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 "Transformations using matrices", we have explained each kind of transformation  step by step explanation along with the corresponding figures.

Transformations - Definition

A very simple definition for transformations is, whenever a figure is moved from one location to another location, a Transformation occurs. 

If a figure is moved from one location another location, we say, it is transformation. Our next question is, how can we do the transformation using matrices?. To know that, we have to be knowing the different types of transformations.

Now, let us come to know the different types of transformations.

Different types of "Transformations" using matrices

There are four main types in transformations using matrices. They are

                          1. Reflection

                          2. Rotation

                          3. Translation

                          4. Dilation

What is "Image" and "Pre-image"?

When a transformation occurs, the original figure is known as the pre-image and the new figure is known as the image.

It has been clearly shown in the below picture.

Rigid transformation or Isometry

A transformation where the pre-image and image are congruent is called a rigid transformation or an isometry.

It has been clearly shown in the below picture.

When a figure is moved from one location to another location, we say that it is a transformation.

In this point, always students have a question.

That is, if a figure is moved from one location to another location, we say, "it is transformation". How can this transformation made using matrices?

More clearly, on what grounds is the transformation made?

Is there any pre-decided rule to make transformation?

Yes, there is a pre-decided rule to make each and every transformation.

The rule we apply to make transformation is depending upon the kind of transformation we make.

We have already seen that there are four main type of transformations.They are reflection, rotation, translation and dilation. 

For example, if we are going to make transformation using reflection, there is a pre-decided rule for that. According to the rule, we have to make transformation.

The rule we apply to make transformation using reflection and the rule we apply to make transformation using rotation.

Hence, for each type of transformation, we may have to apply different rule.