[Maths Class Notes] on Transformations Pdf for Exam

In normal words transformation means a mathematical function. You can say that a transformation is the invertible function from any set X to its own set X or any other set Y. For any term the transformation may simply indicate that the geometric aspect of this particular function is considered. Further these transformations are of many types. In layman’s terms you can say that’s means just taking a preimage and then transforming it or producing it into an actual image.

Thus when an object is transformed from its one form to another form then both the object and image can be congruent or they can be just similar.

When the  shape of an object can easily be transformed to another shape just by using turns, flips or slides then both the shapes can be known as congruent while when one shape needs to be resized to form the another shape then we can refer to it as similar shapes.

This article provided to you by will help to clear your doubts and queries related to the topic transformations. At our main goal is to make the students proud of any topic they learn, so in order to be well aware of the topic, the students are provided with frequently asked questions at the end of this article in order to clear most of their queries regarding the topic Transformation.

In this article you are going to learn about this topic transformation in mathematics which is the base of your mathematics if higher classes. In this article the topics that you will come across  are transformation, definition of transformation , categories of Transformation,types of transformation and finally the conclusion. Let’s have a look at this article in order to get a better knowledge of the transformation topic.

In geometrical terms, when objects move in the coordinate plane, they go through transformations. In other terms, a set of coordinate points change into a different set of coordinates by the process of transformation. As in English, “transformation” means “to change,” in geometry, it refers to changes in the geometric properties of an object. There are different kinds of transformations that can occur; some of them do not change the size of the object while some of the transformations resize the original object. We will look at the different kinds of transformation in this article with examples.

Definition of Transformation

One can perform different operations on any image in a plane to transform it. In the process of transformation, an object can change its size, position, or orientation. It involves taking a pre-image of an object and producing its image with a transformation of some sort. 

Categories of Transformation

A transformation can be broadly categorised into 2 different types:

Rigid or isometric Transformation – The transformation in which size of the pre-image is unchanged is called a rigid transformation. If you look at this transformation then you are not going to find any change in the  form,that is the shape and size of the object.

Non-Rigid or non-isometric Transformation – A transformation that will change the size, but not the shape of the pre-image is called a non-rigid transformation. If you look at this transformation then you are not going to find any change in the  form,that is the shape and size of the object.

Types of Transformations with Example

Based on how the image is changed, transformations have 5 different types. One of them falls in the non-rigid transformation and the rest are all rigid transformations. As we have studied earlier then rigid involves no change in the actual shape and side whole non rigid involves change 8n its shape and size.

1. Translation (also called slide)

In this type of transformation, the object is only moved in space by sliding it, without any rotation, resizing, etc. There is no change in the object’s dimensions or shape. In translation, every point of the shape must move the same distance and in the same direction. You could use angle-distance or x-y coordinates to translate an object. This is a rigid transformation.  In this transformation before and after the transformation the shape and size is same.Below is a pictorial representation of translation:

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2. Rotation (also called Turn)

In this transformation, the object is turned around a fixed point, called the centre of rotation, either clockwise or anti-clockwise by a certain angle. All the lines of the shape go through the same angle of rotation, changing the orientation and position of the object but not its size or shape. This is a rigid transformation. The distance at any point on the object and the centre remains the same in rotation. Below is an example of rotation:

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3. Reflection (also called Flip)

A mirror image of an object, along a line, is produced by reflection transformation. This line, along which reflection happens, is called the “mirror line,” and all points on the original object, as well as the mirror image, are at the same distance from this line. Reflection does not alter the size or shape of the object, just the position; hence it is again a rigid transformation. You can observer this in the image below:

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4. Glide Reflection

This is a type of reflection in which the final image also goes through a translation. In the figure below, the blue object undergoes a reflection along the centre black axis and then a translation of 6 units down, so glide reflection of the blue object is the pink figure here:

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5. Enlargement (also called dilation)

This is a non-rigid transformation. In this transformation, there is a resizing of the image, but no change in shape. This kind of transformation is also known as compression, expansion, resizing, and contraction. In this, enlargement or reduction in the size of the object happens. The relative sizes of the image, as well as all angles, remain the same. You can see below that the pink figure is the dilated image of the blue figure:

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Conclusion

When a geometric figure is moved around on a coordinate plane, then transformations happen. Transformations do not change the shape of an object but can change its position, size, or orientation. Transformation can be rigid or isometric, where the size of the image does not change, or they can be non-rigid or non-isometric when the size of the image changes due to the transformation. Transformations are mostly done on a coordinate plane, as it makes it easy to count and draw. A common and easiest way of performing transformation is by performing the required operation on the vertices of the preimage, and when you connect the dots, you will be able to get the final transformed image.