If the midpoints of the sides of Delta ABC ar | vedclass

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(B) The area of the triangle formed by joining the midpoints of the sides of a triangle is one-fourth the area of the original triangle.First,calculat

Vedclass · Accepted Answer

$24$

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(B) The area of the triangle formed by joining the midpoints of the sides of a triangle is one-fourth the area of the original triangle.First,calculate the area of $\Delta DEF$ using the coordinates $D(2, 1), E(-2, 3),$ and $F(4, -3)$.Area of $\Delta DEF = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$Area of $\Delta DEF = \frac{1}{2} |2(3 - (-3)) + (-2)(-3 - 1) + 4(1 - 3)|$Area of $\Delta DEF = \frac{1}{2} |2(6) + (-2)(-4) + 4(-2)|$Area of $\Delta DEF = \frac{1}{2} |12 + 8 - 8| = \frac{1}{2} |12| = 6 	ext{ sq units}$.Since $	ext{Area}(\Delta ABC) = 4 	imes 	ext{Area}(\Delta DEF)$,$	ext{Area}(\Delta ABC) = 4 	imes 6 = 24 	ext{ sq units}$.

If the midpoints of the sides of $\Delta ABC$ are $D(2, 1), E(-2, 3),$ and $F(4, -3),$ then find the area of $\Delta ABC$.

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