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).