Triangle XYZ is drawn on a coordinate plane with vertices X(0,0) , Y(3,6) , and Z(4,3) and with medians indicating the midpoint of each line XY , YZ , and ZX . Prove that the medians meet at a single point by finding the centroid.(1 point) centroid= (,)
To find the centroid of triangle XYZ, we need to find the average of the coordinates of its three vertices.
The x-coordinate of the centroid (C) is found by averaging the x-coordinates of X, Y, and Z:
Cx = (0 + 3 + 4)/3 = 7/3
The y-coordinate of the centroid (C) is found by averaging the y-coordinates of X, Y, and Z:
Cy = (0 + 6 + 3)/3 = 3
Therefore, the coordinates of the centroid (C) are (7/3, 3).