If the coordinates of the midpoints of the si | vedclass

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(A) Let the vertices of the triangle be $A(x_1, y_1), B(x_2, y_2)$,and $C(x_3, y_3)$.Given midpoints are $M_1(4, 2), M_2(3, 3)$,and $M_3(2, 2)$.The ce

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$(3, 7/3)$

Vedclass · Answer

(A) Let the vertices of the triangle be $A(x_1, y_1), B(x_2, y_2)$,and $C(x_3, y_3)$.Given midpoints are $M_1(4, 2), M_2(3, 3)$,and $M_3(2, 2)$.The centroid of the triangle formed by the midpoints is the same as the centroid of the original triangle.The centroid $(G)$ of a triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is given by $\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)$.For the triangle formed by midpoints,the centroid is $\left(\frac{4+3+2}{3}, \frac{2+3+2}{3}\right)$.$= \left(\frac{9}{3}, \frac{7}{3}\right) = \left(3, \frac{7}{3}\right)$.

If the coordinates of the midpoints of the sides of a triangle are $(4, 2), (3, 3)$ and $(2, 2)$,what are the coordinates of the centroid?

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