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What We Need To Know About Dilations In Mathematics?

by Steven Brown

Dilation is one type of transformation. You can easily change or resize the shape of an object and image by changing its dimensions. 

With the help of some scaling factors, you can create a new image or object size by using dilation. 

In this article, we will explain some of the necessary factors of dilation that will truly help you in your practical solutions. So let’s move forward to understanding the main thing about dilation

What is meant by dilations?

The dilation transforms any image, shape, object, or figure using scalar factors. The scalar factor is the center point of the figure. 

In mathematics, you can easily resize, increase or decrease the shape by using some dilation properties. 

In simple words, you can say that the figure or shape after dilation is known as “image,” and before dilation or the original shape is “pre-image.”

Thus for the calculation of points of image, you may try this center of dilation calculator, this will provide you with the pathway from pre-image to a complete image.

Types of dilations

Two types of dilation help you transform the object, image, or shape. The detailed description of these two types are:

  1. Enlargement 
  2. Reduction

1. Enlargement

The enlargement in dilation refers to the increase in the size of an image, object, or shape. It is also known as expansion. 

In which the object size is increased with reference to the center point. So the maximum increase in the size of the image is the enlargement. 

2. Reduction

The reduction in dilation is also known as the contraction of the image. In which the scalar factor decreases the size, shape, and image of the object. 

The image shrinks and becomes smaller in the process of reduction. So the decrease in the image is called reduction. 

Both types of dilation will increase or decrease the image size or object, but this transformation remains the same shape and image as the original shape. 

Hence you get a smaller or larger image by dilation in the same shape. 

Dilations with Scale Factor

The scale factor is the center point of the image. It is the ratio of the size of the new image as compare to the size of the old or original image. 

Using the scale factor formula, you can easily figure out the scale factor of dilated shape. Which is defined as: 

Scale Factor = dimensions of the new shape (larger image) ÷ dimensions of the new shape (smaller image). 

This formula will truly help you to understand the scale factor in dilation. The scale factor of a dilated figure may denote by k or r, and some of their key factors are described as follows:

  • When the image size increases or enlarges, then the scale factor is more than 1 means (r > 1)
  • When the image size decreases or contracted, then the scale factor is less than 1 means (r < 1)
  • And when the scale factor is 1 and the image remains the same, then the new image and pre-image are equal to each other. It means ( r = 1) 

Tip: The scale factor can not be zero at any state, and this transformation is based on the scale factor and the center of dilation. 

Features of Dilations in Mathematics

Some of the basic features of dilation in mathematics reveal that few shapes will not change during this process and maintain the distance between points. 

So these features are:

  • The shape remains the same when each angle of the shape is the same.
  • The side midpoints of the shapes are the same as the side midpoints of the dilated or original shape. 
  • The shape remains unchanged when the parallel and perpendicular lines of dilated and original shapes are the same. 
  • When the shape or figures of all images are the same, it also remains unchanged. 

Types of dilations processes

There are two types of dilation process that helps in knowing and changing the image are:

  • Horizontal dilation process
  • Vertical dilation process

1. Horizontal dilation process

The horizontal dilation process is transforming a function with respect to the horizontal factors. In simple words, transformation by a scale factor C and has denoted as Y = f(Cx). 

2. Vertical dilation process

The vertical dilation process is the transformation of a function with respect to vertical factors. The vertical dilation in reference to a scale factor C has denoted as Y = C * f(x). 

These two major dilation processes help transform the distant points and parallel side lines shapes. 

Final Thoughts

The dilation method is the type of transformation that helps concise and enlarge the figure by maintaining the same shape and figure of the object. 

The smaller and larger images can calculate using this dilation process, and it becomes easy to transform them. 

This dilation process has many features and properties that help you in your mathematical calculation. So this article explains everything about dilation that you must need to comeover businesspara

We hope that it helps you in your mathematical calculation and you will conclude with the perfect results. 

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