Question

Find the center of mass (centroid) of the triangle with the vertices (0,0), (9,0), and (0,18) with a density function (x, y) = x² + x + 1.

Answer 1

To find the center of mass (centroid) of a triangle, we need to average the x-coordinates and the y-coordinates of the vertices. For this particular triangle, the center of mass is located at (3,6).

Step-by-step explanation:

To find the center of mass (centroid) of a triangle, we need to first determine the coordinates of the centroid. We can do this by finding the average of the x-coordinates and the average of the y-coordinates of the triangle's vertices. The coordinates of the centroid are given by:

x = (x1 + x2 + x3) / 3

y = (y1 + y2 + y3) / 3

In this case, the vertices of the triangle are (0,0), (9,0), and (0,18). Plugging these values into the formulas, we get:

x = (0 + 9 + 0) / 3 = 9/3 = 3

y = (0 + 0 + 18) / 3 = 18/3 = 6

Therefore, the center of mass (centroid) of the triangle is located at the coordinates (3,6).