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Get the free Dilation Worksheet and other resources for teaching & understanding Dilations

## Here’s How to Dilate in Math

Dilation Definition in Math involves enlarging or shrinking figures on a coordinate grid. Dilation on a Coordinate Grid takes place when a figure is multiplied by a Scale Factor. The scale factor tells you if the figure is going to get larger or smaller If the scale factor is greater then one, the figure will get larger. If the scale factor is less then one, the figure will get smaller. You can Dilate on a Coordinate Grid by multiplying the coordinates of the figure by the scale factor. The last step for Dilation on a Coordinate Grid is to write the coordinates of the new location of the figure.

Common Core Standard: 8.G.4

## The short Dilation Definition in Math

The Center of Dilation is where the dilation will expand from. Typically the Center of Dilation is at the origin, (0,0). However, it can be located anywhere. Our Dilation Worksheet is about Dilating in Math. Dilation definition in math is when you make a figure bigger or smaller. In order to make a figure bigger or smaller, you have to multiply by a scale factor. If the scale factor is larger than one, the figure will get bigger. If the scale factor is less than one, the figure will get smaller. Following our Dilation Worksheet, it shows you that you multiply the scale factor by each coordinate to create the new figure.

## 4 Simple Steps to Dilation in Math Definition

1. When completing a Dilation Worksheet, you must shrink or enlarge a figure.
2. You multiply each coordinate by the scale factor.
3. If the scale factor is above one, the figure gets larger.
4. If the scale factor is under one, the figure gets smaller.

## Dilation in Math Practice Problems Quiz

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Dilation Quiz

Click Start to begin the practice quiz!

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Find the coordinate after a dilation with a scale factor of 2.

(3,4)

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Find the coordinate after a dilation with a scale factor of 3.

(5,7)

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Find the coordinate after a dilation with a scale factor of 1/4.

(-8,-4)

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Find the coordinate after a dilation with a scale factor of 1/2.

(6,4)

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Find the coordinate after a dilation with a scale factor of 4.

(1,8)

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## A Quick Video where we complete our Dilation Worksheet

Watch our free video on how to solve Dilations. This video shows how to solve problems that are on our free Dilation worksheets that you can get by submitting your email above.

Watch the free Dilation video on YouTube here: Dilation Worksheet Video

Video Transcript:

This video is about our dilations worksheet. You can get this dilation worksheet for free by clicking on the link in the description below.

Dilation in math refers to either making a figure larger or making a figure smaller which is the dilation math definition. It’s a way to transform a figure on a coordinate grid. The way to dilate on the coordinate grid is to multiply all of your coordinates by a scale factor. If the scale factor is greater than 1, if it’s larger than one, your figure will get larger. If the scale factor is less than 1 your figure will get smaller. Most of the questions will ask which graph shows a dilation and you will have to decide on the right answer.

Looking at this square here, if we had a scale factor of let’s say 2 we would multiply all the coordinates by 2 and our figure would get larger. The square after a dilation with the scale factor of 2 would look like this. If we were to dilate our square by 0.5 or ½, the square would get smaller and it would look like this square in green. The way to perform a dilation on the coordinate grid is to take your X and your Y coordinate and multiply it times whatever the scale factor is. So for example if the scale factor was 3 we would take 3 and we would multiply at times X so it would be like 3 X and times y so it would be like 3 Y.

The second problem on our dilation worksheet 8th grade says to graph the figure ABCD after a dilation with a scale factor of 4. We already know that the scale factor is going to be what we use to multiply times all of our coordinates below. In order to do this, we’re going to take each coordinate and multiply it times the scale factor which is 4. For example, in order to get a prime what we have to do is we have to take negative 1 multiply times 4 for our new x-coordinate and then 2 times 4 for a new y-coordinate. So negative 1 times 4 is negative 4 and then two times four is eight. This will be our new a prime.

We will then do that for the remainder of the coordinates. One times four is four. Two times four is eight. One times four is four again. Negative two times 4 is negative eight and then negative two times 4 is negative eight and then negative 1 times 4 is negative 4. In order to graph our new figure we just have to plot these vertices.

I went ahead and copy the new vertices down by the graph. We’re gonna go ahead and plot these. The next step is to draw our lines and create our new figure. You will notice that our new figure is larger and that’s because the scale factor was 4, which is of course greater than 1. This new figure is a solution for the second problem on our dilations on the coordinate plane worksheet.