Question

What are the coordinates of the centroid of a triangle with vertices D(0, 1), E(2, 6), and F(7, 2)?

Answer 1

The centroid of a triangle is the point of intersection of its medians. The medians are the line segments that connect each vertex to the midpoint of the opposite side.

Step-by-step explanation:

The centroid of a triangle is the point of intersection of its medians. The medians are the line segments that connect each vertex to the midpoint of the opposite side.

To find the coordinates of the centroid, you can average the x-coordinates and y-coordinates separately.

Let the coordinates of D(0, 1), E(2, 6), and F(7, 2) be (x1, y1), (x2, y2), and (x3, y3), respectively

The coordinates of the centroid G are given by:

G(x1+x2+x3 / 3 , y1+y2+y3 / 3)

For the given vertices:

G(0+2+7 / 3 , 1+6+2 / 3)

G(9/3 , 9/3)

G(3 , 3)

So, the coordinates of the centroid G are (3, 3).