Questions
If two vertices of a triangle are (-2, 3) and (5, -l), the orthocenter lies at the origin, and the centroid on the line , then the third vertex lies at
a
(7,4)
b
(8, 14)
c
(12,21)
d
None of these
detailed solution
Correct option is D
Suppose that the third vertex is A(h,k) BC is perpendicular to AO because O is orthocenter Hence, kh×-47=-1 4h-7k=0 The centroid of the triangle lies on x+y=7 -2+5+h3,3-1+k3 lies on x+y=7 3+h+2+k=21 h+k=16 solving the above two equations 7k+4k=64 11k=64 k=6411, h=11211 Third vertex is 6411,11211Talk to our academic expert!
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