Assertion: If (0, 3), (1, 1) and (-1, 2) are | vedclass

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(A) Let the vertices of the triangle be $A(x_1, y_1), B(x_2, y_2)$,and $C(x_3, y_3)$.The midpoints of the sides are given as $D(0, 3), E(1, 1)$,and $F

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$A$ and $R$ are both true and $R$ is the correct explanation of $A$.

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(A) Let the vertices of the triangle be $A(x_1, y_1), B(x_2, y_2)$,and $C(x_3, y_3)$.The midpoints of the sides are given as $D(0, 3), E(1, 1)$,and $F(-1, 2)$.The centroid of the triangle formed by the midpoints is the same as the centroid of the original triangle.Centroid of $\Delta DEF = \left( \frac{0 + 1 - 1}{3}, \frac{3 + 1 + 2}{3} \right) = \left( \frac{0}{3}, \frac{6}{3} \right) = (0, 2)$.Since the centroid of the triangle formed by the midpoints is $(0, 2)$,the centroid of the original triangle is also $(0, 2)$.Thus,both Assertion $A$ and Reason $R$ are true,and $R$ is the correct explanation of $A$.

Assertion: If $(0, 3), (1, 1)$ and $(-1, 2)$ are the midpoints of the sides of a triangle,then the centroid of the original triangle is $(0, 2)$.
Reason: The centroid of a triangle and the centroid of the triangle formed by joining the midpoints of the sides of the original triangle are the same.

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Assertion: If $(0, 3), (1, 1)$ and $(-1, 2)$ are the midpoints of the sides of a triangle,then the centroid of the original triangle is $(0, 2)$.Reason: The centroid of a triangle and the centroid of the triangle formed by joining the midpoints of the sides of the original triangle are the same.