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Center of dilation
A fixed point $C$ such that each point of the image lies on the line from $C$ through the original point, and its distance from $C$ is multiplied by the scale factor.
Horizontal dilation
The transformation $y=f(ax)$, where $x$-values are scaled by a factor $\frac{1}{a}$. It is a dilation parallel to the $x$-axis.
Vertical dilation
The transformation $y=a f(x)$, where all $y$-values are multiplied by $a$. It is a dilation with scale factor $a$ parallel to the $y$-axis.