Dilation Rule Calculator

Formula

The formula to calculate the new coordinates after dilation is:

$(x', y') = (k \times x, k \times y)$

Where:

$(x', y')$ are the new coordinates after dilation
$(x, y)$ are the original coordinates before dilation
$k$ is 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.

Example Calculation

Let's consider an example:

Original Coordinates: (3, 4)
Scale Factor (k): 2

Using the formula to calculate the new coordinates after dilation:

$(x', y') = (2 \times 3, 2 \times 4) = (6, 8)$

This demonstrates that with an original point at (3, 4) and a scale factor of 2, the new coordinates after dilation would be (6, 8).