2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 26

  • question_answer
    If a vertex of an equilateral triangle is the origin and the side opposite to it has the equation \[x+y=1,\]then the ortho centre of the triangle is

    A) \[\left( \frac{1}{3},\frac{1}{3} \right)\]    

    B)        \[\left( \frac{\sqrt{2}}{3},\frac{\sqrt{2}}{3} \right)\]

    C) \[\left( \frac{2}{3},\frac{2}{3} \right)\]    

    D)        None of these

    Correct Answer: B

    Solution :

    [b] Clearly, orthocentre 'H' lies on the line \[x-y=0.\] Distance of \[O(0,0)\]from the line \[x+y-1=0\] is \[\frac{1}{\sqrt{2}}\] \[\therefore \,\,\,\,OH=\frac{2}{3}\times \frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{3}\] (In equilateral triangle, centroid coincides with orthocentre) Therefore, orthocentre is \[\left( \frac{\sqrt{2}}{3},\frac{\sqrt{2}}{3} \right)\].


You need to login to perform this action.
You will be redirected in 3 sec spinner