The midpoints of the three sides of a triangl | vedclass

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(D) Let the midpoints be $M_1(1, 2)$,$M_2(-1, 1)$,and $M_3(0, 3)$.The area of the triangle formed by the midpoints of the sides of a triangle is one-f

Vedclass · Accepted Answer

$6$

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(D) Let the midpoints be $M_1(1, 2)$,$M_2(-1, 1)$,and $M_3(0, 3)$.The area of the triangle formed by the midpoints of the sides of a triangle is one-fourth the area of the original triangle.Area of the triangle formed by midpoints $= \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$Area $= \frac{1}{2} |1(1 - 3) + (-1)(3 - 2) + 0(2 - 1)|$Area $= \frac{1}{2} |1(-2) - 1(1) + 0| = \frac{1}{2} |-2 - 1| = \frac{1}{2} |-3| = 1.5 	ext{ sq. units}$.The area of the original triangle $= 4 	imes (	ext{Area of the triangle formed by midpoints}) = 4 	imes 1.5 = 6 	ext{ sq. units}$.

The midpoints of the three sides of a triangle are $(1, 2)$,$(-1, 1)$,and $(0, 3)$. The area of this triangle is (in sq. units):

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