Triangle ABC is drawn on a coordinate plane with vertices A(4,4) , B(9,1) , and C(3,−1) and with medians indicating the midpoint of each of the lines AB , BC , and CA . Prove that the medians meet at a single point by finding the centroid. Express all results in fractions.(1 point) centroid= (,)
To find the centroid of a triangle, we average the coordinates of its vertices.
The coordinates of point A are (4, 4).
The coordinates of point B are (9, 1).
The coordinates of point C are (3, -1).
Summing the x-coordinates and dividing by 3, we find the x-coordinate of the centroid:
(4 + 9 + 3)/3 = 16/3.
Summing the y-coordinates and dividing by 3, we find the y-coordinate of the centroid:
(4 + 1 - 1)/3 = 4/3.
Therefore, the coordinates of the centroid are (16/3, 4/3).