A thin triangular plate of uniform density and thickness has vertices at V1 = (0, 1), v2 = (8, 1), and v3 = (2, 4), as in the figure below, and 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-gram point masses located at the vertices of the plate.
b. Determine how to distribute an additional mass of 6 g at the three vertices of the plate to move the balance point of the plate to (2, 2). [Let w1, w2, and w3 denote the masses added at the three vertices, so that w1 + w2 + w3 = 6.]

4 Metal Plate