Use the Center of Dilation Calculator to find the center of dilation for a given set of points. This calculator is particularly useful in geometry, where dilation is a transformation that alters the size of a figure while maintaining its shape.

## Understanding Dilation

Dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The center of dilation is a fixed point in the plane about which all points are expanded or contracted. The scale factor determines how much the figure is enlarged or reduced.

## How to Use the Center of Dilation Calculator

To use the calculator, you need to input the coordinates of the original point and the dilated point, along with the scale factor. The calculator will then compute the coordinates of the center of dilation using the following formulas:

Center X = (X2 - (X1 * Scale Factor)) / (1 - Scale Factor)

Center Y = (Y2 - (Y1 * Scale Factor)) / (1 - Scale Factor)

Where:

- X1, Y1 are the coordinates of the original point.
- X2, Y2 are the coordinates of the dilated point.
- Scale Factor is the ratio of the size of the image to the size of the original.

## Example Problem

Consider an original point A(2, 3) that is dilated to point B(6, 9) with a scale factor of 2. To find the center of dilation:

- Input the coordinates of point A (2, 3) and point B (6, 9) into the calculator.
- Enter the scale factor of 2.
- Click on “Calculate” to find the center of dilation.

## Applications of Dilation

Dilation is widely used in various fields such as computer graphics, architecture, and art. In computer graphics, dilation helps in resizing images while maintaining their proportions. In architecture, it is used to create scaled models of buildings. Artists use dilation to create larger versions of their sketches or paintings.

## FAQ

**1. What is the scale factor in dilation?**

The scale factor is a number that scales, or multiplies, the dimensions of a figure. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

**2. Can dilation be negative?**

Yes, a negative scale factor will not only change the size of the figure but also reflect it across the center of dilation.

**3. How do I know if my dilation is correct?**

You can verify your dilation by checking if the distances from the center of dilation to the original points and the dilated points are proportional to the scale factor.

**4. Can I use this calculator for multiple points?**

This calculator is designed for individual point pairs. For multiple points, you would need to calculate the center of dilation for each pair separately.

**5. Where can I find more calculators?**