4. A thin triangular plate of uniform density and thickness has vertices at V₁ = (0,3),

V₂ = (4,3), and V3 = (2, 1). The mass of the plate is 3 g.

(a) Find the (x, y)-coordinates of the center of mass of the plate. This balance point

of the plate coincides with the center of mass of a system consisting of three 1 g.

point masses located at the vertices of the plate.

(b) [C] Determine how to distribute an additional mass of 2 g. (so that the plate has

a total mass of 5 g.) at the three vertices of the plate to move the center of mass

to (2, 2).