1. If two vertices of a triangle are (-2,3) and (5,-1). Orthocentre of the triangle lies at the
origin and centroid on the line x+y=7, then the third vertex lies at
A. (7,4)
B. (8,14)
C. (12,21)
D. None of these
Ans: D
Solution: The line passing through the third vertex and orthocentre must be perpendicular to
line through (-2,3) and (5,-1) .Therefore the product of their slope is -1.
Given the two vertices B(-2,3) and C(5,-1); let H(0,0) be the orthocentre ;A(h,k)
Be the third vertex. Then slope of the line through A and H is k/h, while the line
through B & C has the slope (-1-3)/(5+2)=-4/7. By the property of the
orthocentre ,these two lines must be perpendicular ,