Question

Triangle ABC has vertices A (3,-3) B (-7,9) C (-11,3). Determine the point of intersection of the medians, and state the coordinates

Answer 1

(-5, 3)

Explanation:

Let O(x, y) be the centroid of the triangle.

The median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side. There are three medians in a triangle; and the medians of a triangle intersect at a point called the centroid.

The centroid of a triangle is gotten from the average of the x coordinates and the y coordinates of all the three vertices.

For Triangle ABC has vertices A (3,-3) B (-7,9) C (-11,3) and centroid O(x, y). Hence:

`x=(3 + (-7)+(-11))/(3)=-5\\\\y=(-3 + 9 + 3)/(3) =3`

The centroid is at (-5, 3)