A scale factor is a measurement that describes the proportional relationship between the lengths of corresponding sides or dimensions of two similar figures. In the context of dilations, scale factors determine the amount of enlargement or reduction applied to a figure. Let's consider an example: suppose we have a square with side length 4 units and we want to dilate it with a scale factor of 2. To calculate the dimensions of the dilated square, we simply multiply each side length by the scale factor. In this case, the dilated square would have side length 8 units.

It is important to note that scale factors can be greater than 1, which results in enlargement, or less than 1, which leads to reduction. For example, if we dilate a triangle with a scale factor of 0.5, each side length of the dilated triangle will be halved compared to the original triangle.

Scale factors can also be expressed as ratios. Considering a rectangle with a length of 6 units and a width of 3 units, a scale factor of 3:2 indicates that the length will be multiplied by 3 and the width by 2 when dilating the rectangle.

Understanding scale factors is essential in mastering the concept of dilations as they determine the extent of size change in a figure.