How do you find the center of dilation when the original and dilated points are given?

To find the center of dilation when given the original and dilated points, one must consider how dilation works in geometry. A dilation is a transformation that modifies the size of a figure while keeping its shape intact, and it occurs relative to a fixed center point known as the center of dilation.

The center of dilation is crucial because all corresponding points of the original shape and its dilated image will lie on lines that extend from this center. When you draw lines from the center of dilation to each pair of corresponding points (the original and dilated points), these lines will intersect the segment connecting the corresponding points at the center of dilation itself.

This method effectively uses geometric properties, as you need to identify where these lines cross. As such, determining the intersection of the lines that connect each pair of original and dilated points provides a precise location for the center of dilation.

This approach is much more reliable than simply averaging the coordinates or finding the midpoint, as those methods do not account for the actual dilation transformation and can lead to misleading locations. Visually estimating the center is also less precise compared to the systematic method of finding the intersection of lines through the points, which gives an accurate mathematical solution.

Therefore, the correct strategy to find the center of