**Math Calculators** ▶ Dilation Calculator

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**Table of Content**

A free online dilation calculator is specifically designed to calculate the coordinates of the center point of the modified image after it gets transformed from its original size. But before you become familiar with our dilation scale factor calculator, you need to have a more in-depth understanding of some terms. Do not worry as we are going to explain each term in a very easy way for you. So, want to get more knowledge?

Scroll down!

In geometry,

**“A significant transformation in the size of an image without changing its shape is known as dilation.”**

What do you actually see in this picture? Do not panic! Let us tell you what is it!

In the above picture:

- We have a triangle
**ABC**in the coordinate system. - When we perform dilation, we get a new triangle
**A’B’C’**which is the enlarged size of the original triangle. - Note that the shape of the triangle remains the same.

You can trace this change in distance of the coordinates by using our free online dilation calculator.

Generally, we have two types of dilation which are as follows:

**Enlargement:**

When an image gets larger in size just after the dilation is performed, then it is known as enlargement.

**Reduction:**

If there is any contraction in the size of the image after you perform dilation, then it is said to be a reduction.

**Horizontal dilation:**

This type of dilation occurs for a function y = f(x) which dilates the function by a scale factor C using the following equation:

$$ Y = f\left(Cx\right) $$

**Vertical dilation:**

The function y = f(x) dilates vertically wwit a scale factor C using the expression below:

$$ Y = C * f\left(x\right) $$

**“The ratio of the size of the modified image to the original one is known as the scale factor”**

Scale factor actually defines the change in the size of the image. Keep in mind that:

If **SF >1**, the image contracts or gets smaller.

If **0 < SF < 1**, the modified image gets shrinked.

If **SF = 1**, the modified image remains un-altered in both shape and size.

After the dilation is done, the only change that occurs is the change in the distance between the coordinates. Also, you will notice that some factors are not changed during the transformation of the images from their original size to the modified one. These include:

- Each and every angle in the figure remains unchanged.
- Parallel and perpendicular lines also remain the same.
- The midpoints of the sides of both original and dilated images remain the same

You must be thinking that it is going to be something tricky. But believe us it is not. Let us solve some examples so that you understand the dilation properly. Stay focused!

**Example # 01:**

Just suppose we have a triangle **ABC** in the coordinate system. The coordinates of vertices of the triangle are as follows:

$$ A(2, 8), (1, -2), (3, 5) $$

Now, if the scale factor is 5, what is the center of dilation **OA’, OB’, OC’.**

**Solution:**

As the given coordinates are:

$$ A(2, 8), (1, -2), (3, 5) $$

Here we suppose our origin **O(0, 0)** as the center of the original triangle.

Determining the center of dilation as follows:

$$ OA’ = \left(2 * 5, 8 * 5\right) $$

$$ OA’ = \left(10, 40\right) $$

Now we have:

$$ OB’ = \left(1 * 5, -2 * 5\right) $$

$$ OB’ = \left(5, -10\right) $$

Similarly;

$$ OC’ = \left(3 * 5, 5 * 5\right) $$

$$ OC’ = \left(15, 25\right) $$

Here you can also use our free dilations calculator to get immediate results. Believe us the whole process is free of cost!

**Example # 02:**

A square has a center at origin and its corners has coordinates as follows:

$$ A(1, 2), (2, -2), (3, 4), (6, 2) $$

If the scale factor is** ½**, how to find scale factor of dilations?

**Solution:**

As the center of the square is at origin, so we have:

**O(0, 0)**

As we know that:

The points with respect to the origin of the dilated image are **OA’, OB’, OC’, OD’.**

Determining the coordinates of the dilated image.

$$ OA’ = \left(1 * \frac{1}{2}, 2 * \frac{1}{2}\right) $$

$$ OA’ = \left(\frac{1}{2}, 1\right) $$

$$ OA’ = \left(0.5, 1\right) $$

Now:

$$ OB’ = \left(2 * \frac{1}{2}, -2 * \frac{1}{2}\right) $$

$$ OB’ = \left(1, -1\right) $$

$$ OC’ = \left(3 * \frac{1}{2}, 4 * \frac{1}{2}\right) $$

$$ OC’ = \left(\frac{3}{2}, 2\right) $$

$$ OC’ = \left(1.5, 2\right) $$

At last, we have:

$$ OD’ = \left(6 * \frac{1}{2}, 2 * \frac{1}{2}\right) $$

$$ OD’ = \left(3, 1\right) $$

Our free dilation graph calculator is very authentic and widely used by scholars to design various **2D** and **3D** images. If you are one of them and want to take advantage, jump down a little!

**Input:**

- First of all, select the number of inputs (number of points).
- After that, enter x and y coordinates of all the points one by one.
- Enter the dilation which is the scale factor.
- Hit the ‘calculate’ button and here you go!

**Output:**

Our free triangle dilation calculator finds:

- Coordinates of the points of the dilated image with reference at origin.

When a gravitational field causes a change in the time lapse, then it is said to be as gravitational time dilation.

If you multiply the scale factor **½** with the coordinates of the point of the original image, the modified image will shrink for sure. But if you multiply the coordinates of the real image with the scale factor of **6,** the final image gets enlarged.

In applications like thermal expansion and contraction, dilation has a great importance as it is the change in the original position.

Dilation has its branches spread in the galaxy of graphic designing and architecture. Also doctors make a proper use of it for examining a patient’s eye better. To provide firm support to professionals and pupils around the globe, we have developed a free online dilation calculator so that they could get the awesome benefit of this opportunity.

From the source of wikipedia: Scale factor, Dilation

From the source of khan academy: Identify scale factor, Scale copies

From the source of lumen learning: Simultaneity And Time Dilation, Time Dilation, The Twin Paradox.