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Dilation Calculator

Enter the coordinates of the original image and the tool will let you know the coordinates of the final transformed image, with the steps shown.

Number of Input:

Enter the Dilation A:

Enter the Dilation B:

Enter Point

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Our advanced Dilation Calculator helps you find the coordinates of a figure after it is resized. It calculates how points move when a shape is enlarged or reduced. Before using our scale factor calculator, it’s important to understand key concepts about dilation.

What Is Dilation?

In geometry,

“Dilation is a transformation that changes the size of a figure while keeping its shape the same.”

dilation illustration

The image above shows:

A triangle ABC on the coordinate plane.
After dilation, the scaled triangle A’B’C’ is formed.
The shape remains the same; only the size changes.

Our free online Dilation Calculator can track these changes automatically.

Types of Dilation

Dilations are generally of two types:

Enlargement: The image grows larger after dilation.

Reduction: The image becomes smaller after dilation.

Horizontal Dilation: A function y = f(x) stretches or compresses horizontally:

$$ Y = f(Cx) $$

Vertical Dilation: A function y = f(x) stretches or compresses vertically:

$$ Y = C \cdot f(x) $$

What Is Scale Factor in Dilation?

“The scale factor is the ratio of the new image size to the original size.”

The scale factor determines enlargement or reduction:

If SF > 1, the figure enlarges.

enlarged figure

If 0 < SF < 1, the figure reduces in size.

reduced figure

If SF = 1, the figure remains unchanged. Use our scale factor calculator to compute this instantly.

Characteristics of Dilation

During dilation, distances between points change, but some properties remain constant:

All angles stay the same.
Parallel and perpendicular lines remain unchanged.
Midpoints of sides remain proportionally aligned.

How to Find the Scale Factor of a Dilation

Here are step-by-step examples:

Example 1:

Triangle ABC with vertices:

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

Scale factor = 5

Solution:

Using origin O(0,0) as center:

$$ A' = (2*5, 8*5) = (10, 40) $$

$$ B' = (1*5, -2*5) = (5, -10) $$

$$ C' = (3*5, 5*5) = (15, 25) $$

The dilated triangle coordinates are A'(10,40), B'(5,-10), C'(15,25).

Example 2:

Square centered at origin with vertices:

$$ A(1, 2), B(2, -2), C(3, 4), D(6, 2) $$

Scale factor = ½

Solution:

$$ A' = (1*0.5, 2*0.5) = (0.5, 1) $$

$$ B' = (2*0.5, -2*0.5) = (1, -1) $$

$$ C' = (3*0.5, 4*0.5) = (1.5, 2) $$

$$ D' = (6*0.5, 2*0.5) = (3, 1) $$

How the Dilation Calculator Works

Our calculator is useful for students, designers, and engineers to scale 2D and 3D figures precisely.

Input:

Choose number of points.
Enter x and y coordinates for each point.
Provide the scale factor.
Click “Calculate.”

Output:

Coordinates of the transformed figure relative to the origin.

FAQs

What is gravitational time dilation?

Gravitational time dilation occurs when time moves slower in stronger gravitational fields compared to weaker fields.

How does scale factor ½ differ from 6?

A scale factor of ½ reduces the figure, while a scale factor of 6 enlarges it significantly.

What is the use of dilation in chemistry?

Dilation is applied in physics and chemistry for thermal expansion calculations, where materials expand or contract due to temperature changes.

Conclusion

Dilation is essential in geometry, architecture, graphic design, and medical imaging. Professionals and students use dilation calculations to resize figures accurately. Our free online Dilation Calculator makes this process fast, accurate, and easy to understand.

References

From Wikipedia: Scale factor, Dilation From Khan Academy: Scale copies From Lumen Learning: Time Dilation, Twin Paradox.

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