If (0, 0), (1, 2), and (-3, 4) are the midpoi | vedclass

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(B) Let the midpoints be $D(0, 0), E(1, 2),$ and $F(-3, 4)$.The area of triangle $DEF$ is given by the formula:Area $= \frac{1}{2} |x_1(y_2 - y_3) + x

Vedclass · Accepted Answer

$20$

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(B) Let the midpoints be $D(0, 0), E(1, 2),$ and $F(-3, 4)$.The area of triangle $DEF$ is given by the formula:Area $= \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$Area of $\Delta DEF = \frac{1}{2} |0(2 - 4) + 1(4 - 0) + (-3)(0 - 2)|$$= \frac{1}{2} |0 + 4 + 6| = \frac{1}{2} 	imes 10 = 5$.The area of triangle $ABC$ is $4$ times the area of the triangle formed by joining the midpoints.Area of $\Delta ABC = 4 	imes 	ext{Area of } \Delta DEF = 4 	imes 5 = 20$.

If $(0, 0), (1, 2),$ and $(-3, 4)$ are the midpoints of the sides of a triangle $ABC$,find the area of triangle $ABC$.

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