To calculate the dilation of a shape, you need to understand the concept of dilation in geometry. Dilation is a transformation that alters the size of a shape but maintains its proportions. This means that the shape can grow larger or shrink smaller while keeping the same shape and angles. The dilation is determined by a scale factor, which is a number that indicates how much the shape will be enlarged or reduced.

For example, if you have a scale factor of 2, every point of the shape will be moved away from the center of dilation by a distance that is twice as far as its original position. Conversely, a scale factor of 0.5 would bring every point closer to the center of dilation, effectively reducing the size of the shape by half.

To use the dilation calculator, you will need to input the scale factor and the original coordinates of the shape. The calculator will then compute the new coordinates after dilation. This is particularly useful in various fields such as architecture, graphic design, and any area where precise measurements and transformations are necessary.

Dilation Formula

The formula for calculating the dilated coordinates is as follows:

Dilated Coordinates = (x * Scale Factor, y * Scale Factor)

Where:

  • Dilated Coordinates are the new coordinates after applying the dilation.
  • Original Coordinates are the coordinates of the shape before dilation.
  • Scale Factor is the factor by which the shape is enlarged or reduced.

For instance, if the original coordinates of a triangle are (1, 2), (3, 4), and (5, 6) and the scale factor is 2, the new coordinates will be (2, 4), (6, 8), and (10, 12) respectively.

Applications of Dilation

Dilation has numerous applications in real life. In art, artists often use dilation to create larger or smaller versions of their work while maintaining the same proportions. In architecture, dilation can help in scaling blueprints to fit different sizes of buildings. In computer graphics, dilation is used to resize images and shapes while preserving their aspect ratios.

Example Problem

Consider a rectangle with original coordinates (2, 3) and (4, 5). If we apply a scale factor of 3, the new coordinates will be calculated as follows:

  • For the point (2, 3): (2 * 3,