How do you calculate the output of a dilation applied to multiple points?

To determine the output of a dilation applied to multiple points, you need to understand the fundamental concept of dilation in geometry. Dilation involves resizing a figure while maintaining its shape. This process uses a scale factor, which determines how much larger or smaller the new points will be compared to the original points.

When you have multiple points and you apply a dilation, you take the coordinates of each point and multiply them by the scale factor. Mathematically, if you have a point with coordinates (x, y) and you want to dilate it by a scale factor of k, the new coordinates after dilation will be (kx, ky). This applies individually to each point.

This method ensures that all points move away from (or towards) the center of dilation proportionally, preserving the overall shape and proportions of the figure being transformed. Hence, applying the scale factor to each point's coordinates correctly gives the resultant positions of the points after dilation.