question_answer

The orthocentre of the triangle formed by (8,0) and (4, 6) with the origin, is:

A)  \[\left( 4,\frac{8}{3} \right)\]                    

B)  \[(3,-4)\]            

C)         \[(4,3)\]             

D)         \[(3,4)\]

E)  \[\left( \frac{8}{3},4 \right)\]

Correct Answer: A

Solution :

Line perpendicular to OA passing through B is \[x=4\]. Line perpendicular to AB through origin is \[y=\frac{2}{3}x\] \[\therefore \]Intersection point of\[x=4\]and\[y=\frac{2}{3}x\]is\[\left( 4,\frac{8}{3} \right)\]. \[\therefore \]Orthocentre of triangle is\[\left( 4,\frac{8}{3} \right)\].