CALCULATOR

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## Dilation on a Graph Calculator

### Step 1. Identify the center of dilation.

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.When we dilate shapes on a grid, we need to know the center of dilation and the scale factor. or explore our and sections to learn more about dilations on a graph and test your understanding.

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 👯♀️.

To help us understand these terms, let’s imagine we have a movable screen and a fixed projector that can’t be moved:

### Closer

✨ Drag to move the projection ✨

### Farther

The center of dilation is like the fixed projector: it’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

Lesson

Practice

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.

$original points=(x_{1},y_{1}),(x_{2},y_{2}),...,(x_{n},y_{n})$

### 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 points×scale factor(x_{original},y_{original})×scale factor =new points=(x_{new},y_{new}) $

Original Point | $×$ | Scale Factor | $=$ | New Point |

$(x_{1},y_{1})$ | $×$ | $s$ | $=$ | $(x_{1}×s,y_{1}×s)$ |

$(x_{2},y_{2})$ | $×$ | $s$ | $=$ | $(x_{2}×s,y_{2}×s)$ |

$...$ | $×$ | $s$ | $=$ | $...$ |

$(x_{n},y_{n})$ | $×$ | $s$ | $=$ | $(x_{n}×s,y_{n}×s)$ |

### Step 5. Plot the new points to get the dilated shape.

LESSON

— Dilations Centered at the Origin

PRACTICE

— Dilations Centered at the Origin

LESSON

— Dilations NOT Centered at the Origin

PRACTICE

— Dilations NOT Centered at the Origin

CONCLUSION

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