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The coordinates of the midpoints of the sides of a triangle ABC are D(2, 1), E(5, 3) and F(3,7)Equation of median of the triangle ABC passing through F is(A) 10x + y-37=o(B) x + y-10=0(C) x-10y + 67= 0(D) none of these

Answer»

Let the vertices be A(x1, y1), B(x2, y2) and C(x3, y3)

Let D, E, and F be the midpoints of AB, BC and AC respectively.

D(2, 1), E(5, 3) and F (3, 7)

x1 + x2 = 4 and y1 + y2 = 2

x2 + x3 = 10 and y2 + y3 = 6

x3 + x1 = 6 and y1 + y3 = 14

x3 = 6 - x1 and x2 = 4 - x1

6 - x1 + 4 - x1 = 10 or x1 = 0

x2 = 4 and x3 = 6

y2 = 2 - y1 and y3 = 14 - y1

16 - 2y1 = 6 or y1 = 5

y2 = - 3 and y3 = 9

Therefore, the co-ordinates are (0, 5), (4, - 3) and (6, 9)

Equation of AB: (y - 5) = (-3 - 5)/(4 - 0)[x - 0]

Or, 4y - 20 = - 8x

Or, y + 2x = 5

Equation of BC: (y - 9) = (- 3 - 9)/(4 - 6)[ x - 4]

Or, 18 - 2y = - 12x + 48

Or, 6x - y = 15

Equation of AC: (y - 5) = (9 - 5)/(6 - 0)[x - 0]

Or, 6y - 30 = 4x

Or, 2x + 3y = 15

wrong answer


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