question_answer

If two sides of a  triangle are represented by \[{{x}^{2}}-7xy+6{{y}^{2}}=0\] and the centroid is (1, 0) then the equation of third side is

A)            \[2x+7y+3=0\]                     

B)            \[2x-7y+3=0\]

C)            \[2x+7y-3=0\]                      

D)            \[2x-7y-3=0\]

Correct Answer: D

Solution :

           Given two lines are \[x-6y=0\] and \[x-y=0\]. We know \[\frac{0+{{x}_{1}}+{{x}_{2}}}{3}=1\]            \[\Rightarrow {{x}_{1}}+{{x}_{2}}=3\]            .....(i)                    and \[{{y}_{1}}+{{y}_{2}}=0\]     .....(ii)                    Also \[{{x}_{1}}-6{{y}_{1}}=0\] .....(iii)                   \[{{x}_{2}}-{{y}_{2}}=0\]               .....(iv)                    [Since the point (x1,y1) and \[({{x}_{2}},{{y}_{2}})\]lies on the lines AB and AC respectively]                    Now on solving, the coordinates of B and C are \[\left( \frac{18}{5},\frac{3}{5} \right)\]and \[\left( \frac{-3}{5},\frac{-3}{5} \right)\]respectively.                    Hence the equation of third side i.e., BC is \[2x-7y-3=0\].