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

Analytically: translate the center to the origin, shrink everything, translate back.
Geometrically: move the points on each line through the center toward the center by decreasing length by a factor $0.7$.
This changes all lengths to 70% of what they were. It will fix whatever point you have decided is the "center" - probably the intersection of the medians. For areas, use factor $\sqrt{0.7}$. 
