Answer to Question #176674 in Calculus for Joshua

Question

Find the center of mass for the triangle with vettices (0,0), (-4,2) and (0,6).

Answer 1

Initial data: A(–4,2), B(0,6), O(0,0).

Need to find: coordinates of point C, where C is the center of mass for the triangle AOB.

Decision. Let's make a drawing of the AOB triangle according to the given coordinates of its vertices (see Picture 1).

It is known that point C will lie at the intersection of the medians of a given triangle. In this case, these are the medians AH and OK. Their intersection will give the desired center of mass C.

The coordinates of this point are determined by the well-known formulas:

x_C=(x_A+x_O+x_B)/3, y_C=(y_A+y_O+y_B)/3.

Making calculations using these formulas, we get:

x_C=(–4+0+0)/3=–4/3, y_C=(2+0+6)/3=8/3.

Answer: x_C=–4/3, y_C=8/3.