Dilations change the size and shape of figures in some clear ways:

1. Size Change: A shape can get bigger or smaller depending on a number called the scale factor, $k$.

   • If $k > 1$, the shape gets bigger.
   • If $0 < k < 1$, the shape gets smaller.

2. Proportionality: Every side of the shape is multiplied by that scale factor. For example, if a triangle has sides that are 3, 4, and 5 units long, and we use a scale factor of $k = 2$, the new side lengths will be 6, 8, and 10 units.

3. Area Change: The area of a shape changes by multiplying it by $k^2$. So if the original area is $A$, the new area after dilation is $k^2 \cdot A$. For instance, if $k = 2$ and the original area $A = 12$, the new area would be 48.