Dilation in geometry means a transformation in the size of an object, but not the shape, using a central axis point. A simple example is a right-angled triangle, where you use the central axis point as the place where the vertical line meets the horizontal line at 90 degrees. If you increase both lines equally, the size of the triangle changes, but the shape and angles remain the same.
Scaling is the term used in conjunction with dilation to determine the size of a dilated object compared to its original size. An object that is dilated to twice its original size has a scaling of 2; similarly, an object dilated to three times its original size has a scaling of 3. Scaling is based on the increase in the length of the lines that connect the central point.
Using a right-angle triangle as an example, assume that the original triangle has a vertical and horizontal line each measuring 2 inches and the axis point is where the two lines meet. If you extend both lines by 2 inches, the triangle dilates to double the size and the scaling is 2. Extend both lines another 4 inches, making the length of each line 8 inches, and the triangle dilates to four times its original size and has a scaling of 4.
The axis point is the place lines extend from. Theoretically, as the lines must be straight, they can extend infinitely. Calculations to determine the dilation of a specific object are also infinite. However, the axis point doesn’t have to be on the actual object; it can be a distance away from it. For example, if the axis point on a right-angle triangle is outside the triangle, then you would draw three lines from the axis point that connect to and extend past the points of the triangle. As long as you measure exactly the same distance along each line, the object increases in size, but remains exactly the same shape.