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Dilations on a Graph Calculator

QUICK LINKS


Dilations on a Graph Calculator

CALCULATOR
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Dilation on a Graph Calculator

Step 1. Identify the center of dilation.

Imagine the center of dilation as the fixed location of a projector.

Step 2. Identify the original points of the polygon.

How many points does the shape have?
Imagine this as an image projected onto a screen by the projector.

Step 3. Identify the scale factor .

What is the scale factor?

We have some questions for you! Help us out through this
INTRO
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A dilation is a transformation that changes the size of an image without changing its shape or proportions.
It's like how when Ant-Man gets bigger or smaller, each body part changes size by the same amount, so he looks the same - just bigger or smaller than before. Dilating shapes is similar ๐Ÿ‘ฏโ€โ™€๏ธ.
When we dilate shapes on a grid, we need to know the center of dilation and the scale factor.
To help us understand these terms, letโ€™s imagine we have a movable screen and a fixed projector that canโ€™t be moved:

Closer

โœจ Drag to move the projection โœจ

Farther

The center of dilation is like the fixed projector: itโ€™s a fixed point from which the image is drawn. The scale factor determines how much smaller or larger the dilated image will be.
If the scale factor is , we can imagine keeping the distance between the projector and the screen the same, which will make the new image the same as the original.
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about dilations on a graph and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

KEY STEPS
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How to Perform Dilations

Step 1. Identify the center of dilation.

Imagine this as the fixed location of the projector.

Step 2. Identify the original points of the polygon.

Imagine this as the original image before the screen is moved.

Step 3. Identify the scale factor .

If the scale factor is , we can imagine keeping the distance between the projector and the screen the same, which will make the new image the same as the original.

Step 4. Multiply each original point of the polygon by the scale factor to get the new points.

Original PointScale FactorNew Point

Step 5. Plot the new points and connect the dots to get your dilated shape.

Step 4. Find the difference between the and values of each original point and the center of dilation .

Imagine this as finding the distance from the projector to the screenโ€™s original position.
Original PointCenter of DilationDifference

Step 5. Multiply each difference by the scale factor.

Imagine this as finding the new distance from the projector to where the screenโ€™s new position will be.
DifferenceScale FactorNew Difference

Step 6. Add the new difference to the center of dilation to get the new points.

Imagine this as finding the position of the new image.
New DifferenceCenter of DilationNew Point

Step 7. Plot the new points and connect the dots to get your dilated shape.

LESSON
โ€” Dilations Centered at the Origin
PRACTICE
โ€” Dilations Centered at the Origin
LESSON
โ€” Dilations NOT Centered at the Origin
PRACTICE
โ€” Dilations NOT Centered at the Origin
CONCLUSION
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