The coordinates of ∆LMN are L(4,7), M(6, −1), and N(−2,3).Algebraically, solve the system of equations represented by the medians
to determine the location of the centroid of ∆LMN.
To find the centroid of a triangle, we need to calculate the average of the x-coordinates and the average of the y-coordinates of its three vertices. In other words:
Centroid_x = (L_x + M_x + N_x) / 3
Centroid_y = (L_y + M_y + N_y) / 3
where L_x and L_y are the x and y coordinates of vertex L, and so on.
So let's plug in the coordinates of the three vertices:
Centroid_x = (4 + 6 - 2) / 3 = 2
Centroid_y = (7 - 1 + 3) / 3 = 3
Therefore, the centroid of triangle LMN is located at the point (2,3).