In mathematics, transformations are a fundamental concept that allow us to manipulate and change geometric shapes. One important type of transformation is a dilation. A dilation is a transformation that uniformly scales a figure by a factor, either enlarging or reducing its size.

To understand dilations, let's consider an example. Imagine we have a triangle with side lengths 2 cm, 3 cm, and 4 cm. If we dilate this triangle by a factor of 2, all the side lengths of the new triangle will be twice as long as the original. Therefore, the new triangle will have side lengths of 4 cm, 6 cm, and 8 cm. Similarly, if we dilate the triangle by a factor of 0.5, all the side lengths will be half of the original, resulting in side lengths of 1 cm, 1.5 cm, and 2 cm.

Dilations can also occur with respect to a center point. If the center of dilation is outside the shape, the shape will either expand or shrink. On the other hand, if the center of dilation is inside the shape, the shape will be compressed or expanded depending on the scale factor.

Dilations have various real-life applications. Architects and engineers use dilations to scale building plans. Artists use dilations to create different sizes of their artwork. Understanding dilations will enable us to analyze and interpret the changes in size and shape that occur in the real world.