133k views
2 votes
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.

1 Answer

2 votes

Final answer:

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).

User Ondrej
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories