In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is 2x +y = 4. Let the point B lie on the line x + 3y = 7. If (a, b) is the centroid of $\Delta ABC,$  then 15(a + b) is equal to:

Correct Option - 3


Detailed Solution:

  $\begin{array}{l}2x+y=4\\ 2x+6y=14\end{array}\}y=2,x=3$              

B (1, 2)

Let C (k, 4 – 2k)

Now AB² = AC²

->5k² – 24k + 19 = 0

$\alpha =\frac{6+1+\frac{10}{5}}{3}=\frac{18}{5}$    

Now 15 (a + b)

$15\left(\frac{17}{5}\right)=51$                

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