Question

Two vertices of a triangle are `(5,-1)` and `(-2, 3)`. If the orthocentre of the triangle is the origin, then the third vertex is
A. `(4,7)`
B. `-4,-7)`
C. `(2,-3)`
D. `(5,-1)`

Answer 1

Correct Answer - B
Let O (0,0) be the orthocentre , `A(x_(1),y_(1))` be the third vertex, and B(-2,b) and C (5,-1) be other two vertices of the given triangle . Then,
`OA bot Bc rArr (y_(1)-0)/(x_(1)-0) xx (-1-3)/(5+2) = - 1 rArr 7 x_(1)= 4y_(1)" ".....(i)`
and, `OB bot AC rArr (3)/(-2)xx(-1-y_(1))/(5-x_(1)) = - 1 rArr 2x_(1) - 3y_(1)= 13" ".....(ii)`
Sloving (i)and (ii), we get `x_(1) = - 4, y_(1) = - 7`
Thus, the orthocentre is (-4,-7)