If D, E, and F are the midpoints of the sides | 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 of the area of the original triangle.First,calcu

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$2.5$

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(B) The area of the triangle formed by joining the midpoints of the sides of a triangle is one-fourth of the area of the original triangle.First,calculate the area of $\Delta ABC$ using the coordinates $A(5, -1), B(-7, 6),$ and $C(1, 3)$.Area of $\Delta ABC = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$$= \frac{1}{2} |5(6 - 3) + (-7)(3 - (-1)) + 1(-1 - 6)|$$= \frac{1}{2} |5(3) - 7(4) + 1(-7)|$$= \frac{1}{2} |15 - 28 - 7|$$= \frac{1}{2} |-20| = 10 	ext{ sq. units}$.Since the area of $\Delta DEF = \frac{1}{4} 	imes 	ext{Area of } \Delta ABC$,Area of $\Delta DEF = \frac{1}{4} 	imes 10 = 2.5 	ext{ sq. units}$.

If $D, E,$ and $F$ are the midpoints of the sides $AB, BC,$ and $CA$ of the triangle formed by the points $A\ (5, -1), B\ (-7, 6),$ and $C\ (1, 3)$ respectively,find the area of $\Delta DEF$.

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