15. A thin triangular plate of uniform density and thickness has vertices at \( \mathbf{v}_{1}=(3,3), \mathbf{v}_{2}=(7,3), \mathbf{v}_{3}=(4,6) \), as in the figure to the right, and the mass of the plate is 3 g . Complete parts \( a \) and \( b \) below.
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.
The center of mass of the plate is located at \( \square \)
(Type an ordered pair. Type integers or simplified fractions.)
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 \( (4,4) \). [Hint: Let \( \mathrm{w}_{1}, \mathrm{w}_{2}, \mathrm{w}_{3} \) denote the masses added at the three vertices, so that \( \mathrm{w}_{1}+\mathrm{w}_{2}+\mathrm{w}_{3}=6 \).]
Add \( \square \) g at \( (3,3) \), add \( \square \) g at \( (7,3) \) and add \( \square \) g at \( (4,6) \).
(Type integers or decimals rounded to one decimal place as needed.)
