If the coordinates of the midpoints of Delta | vedclass

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(C) Let the vertices of $\Delta ABC$ be $A(x_1, y_1), B(x_2, y_2),$ and $C(x_3, y_3).$ The midpoints of the sides are given as $D(4,6), E(2,2),$ and $

Vedclass · Accepted Answer

$(3,3)$

Vedclass · Answer

(C) Let the vertices of $\Delta ABC$ be $A(x_1, y_1), B(x_2, y_2),$ and $C(x_3, y_3).$ The midpoints of the sides are given as $D(4,6), E(2,2),$ and $F(3,1).$ The centroid of a triangle formed by the midpoints of the sides of a triangle is the same as the centroid of the original triangle. The centroid $(G)$ of $\Delta DEF$ is given by the formula: $G = \left( \frac{x_D + x_E + x_F}{3}, \frac{y_D + y_E + y_F}{3} \right).$ Substituting the given values: $G = \left( \frac{4 + 2 + 3}{3}, \frac{6 + 2 + 1}{3} \right).$ $G = \left( \frac{9}{3}, \frac{9}{3} \right) = (3, 3).$ Thus,the coordinates of the centroid of $\Delta ABC$ are $(3, 3).$

If the coordinates of the midpoints of $\Delta ABC$ are $D(4,6), E(2,2),$ and $F(3,1),$ then find the coordinates of the centroid of $\Delta ABC$.

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