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

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.

  1. First, determine the original coordinates (x, y).
  2. Next, determine the scale factor (k).
  3. Next, use the formula (x’, y’) = (k * x, k * y) to calculate the new coordinates after dilation.
  4. Finally, calculate the Dilation Rule.
  5. 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