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

Two vertices of a triangle are `(5,-1)` and `(-2, 3)`. If the orthocen

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

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

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