Dilation, shrink a triangle by $30\%$ I would like to know how I shrink a triangle by $30\%$ using dilation not changing its center?

I presume you want to shrink the Area by $30\%$.
Assume the center is at $p$. Then you start by translating the triangle so that its center is in $0$, and then note that the area scales like the square of the scaling factor, so you have to scale the coordinates by $\sqrt{0.7}$, and then translate it back to its original position.
Composing these maps gives:
$$f(\vec{x})=\sqrt{0.7}\ (\vec{x}-\vec{p})+\vec{p}$$
