Enter the original coordinates and scale factor into the calculator to determine the new coordinates after dilation.

- Center of Mass Calculator (X,Y coordinates)
- Polar Coordinates Calculator
- Inner Reflection Coefficient Calculator

## Dilation Rule Formula

The following formula is used to calculate the new coordinates of a point after dilation.

(x', y') = (k * x, k * y)

Variables:

- (x’, y’) are the new coordinates after dilation
- (x, y) are the original coordinates before dilation
- k is the scale factor

To calculate the new coordinates after dilation, multiply the original x-coordinate and the original y-coordinate by the scale factor. The result will be the new coordinates of the point after dilation. If the scale factor is greater than 1, the figure enlarges; if it’s between 0 and 1, the figure reduces in size. The distances between points in the figure are proportionally increased or decreased according to the scale factor.

## What is a Dilation Rule?

A dilation rule in mathematics refers to a transformation that alters the size of a figure without changing its shape. It involves expanding or shrinking the figure from a fixed point, known as the center of dilation. The degree of dilation is determined by a scale factor. If the scale factor is greater than 1, the figure enlarges; if it’s between 0 and 1, the figure reduces in size. The distances between points in the figure are proportionally increased or decreased according to the scale factor.

## How to Calculate Dilation Rule?

The following steps outline how to calculate the Dilation Rule.

- First, determine the original coordinates (x, y).
- Next, determine the scale factor (k).
- Next, use the formula (x’, y’) = (k * x, k * y) to calculate the new coordinates after dilation.
- Finally, calculate the Dilation Rule.
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem : **

Use the following variables as an example problem to test your knowledge.

Original coordinates (x, y) = (3, 5)

Scale factor (k) = 2