What is the method for performing a dilation on a set of coordinates?

Dilation is a transformation that alters the size of a shape while keeping its proportions intact. When performing a dilation on a set of coordinates, the process involves multiplying both the x and y coordinates of the point by a scale factor. This scale factor determines how much larger or smaller the shape will appear.

For example, if you have a point (x, y) and you wish to dilate it by a scale factor of k, the new coordinates after the dilation will be (kx, ky). If k is greater than 1, the shape enlarges, while a value between 0 and 1 will reduce the size of the shape.

This method preserves the geometric relationships among points, meaning that the angles and relative proportions remain the same, while the overall size changes based on the scale factor used. Thus, multiplying both coordinates by the scale factor is the correct method for performing a dilation.