A thin triangular plate of uniform density and thickness has vertices at v = (2,1), V...

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A thin triangular plate of uniform density and thickness has vertices at v₁ = (2,1), V₂ = (8,1), v3 = (4,7), as in the figure to the right, and the mass of the plate is 3 g. Complete parts a and b below. Ay 10- 8- 6- 4. 2- 0+ 0 V10 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. 14 ,3 V3 2 4 t6 •V₂ 8 10 The center of mass of the plate is located at (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 (4,3). [Hint: Let w₁, W₂, W3 denote the masses added at the three vertices, so that w₁ + W₂ + W3 = 6.] Add gat (2,1), add g at (8,1) and add g at (4,7). (Type integers or decimals rounded to one decimal place as needed.) X Ⓡ N A thin triangular plate of uniform density and thickness has vertices at v₁ = (2,1), V₂ = (8,1), v3 = (4,7), as in the figure to the right, and the mass of the plate is 3 g. Complete parts a and b below. Ay 10- 8- 6- 4. 2- 0+ 0 V10 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. 14 ,3 V3 2 4 t6 •V₂ 8 10 The center of mass of the plate is located at (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 (4,3). [Hint: Let w₁, W₂, W3 denote the masses added at the three vertices, so that w₁ + W₂ + W3 = 6.] Add gat (2,1), add g at (8,1) and add g at (4,7). (Type integers or decimals rounded to one decimal place as needed.) X Ⓡ N

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