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Q.

If in triangle ABC, A = (1, 10), circumcenter = (-1/3,2/3), and orthocenter = (11/4 , 4/3), then the coordinates of the midpoint of the side opposite to A are

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a

(1, -11/3)

b

(1, 5)

c

(1, -3)

d

(1,6)

answer is A.

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Detailed Solution

Circumcenter O=(-1/3, 2/3) and orthocenter H = (11/3,4/3).Therefore, the coordinates of G are (1,8/9). Now, the pointA is (1, 10) as G is (1 ,8/9). Hence,AD:DG = 3:1∴Dx=3−12=1,Dy=(8/3)−102=−113Hence, the coordinates of the midpoint of BC are (1, -11/3).
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