Two equal sides of an isosceles triangle are along − x + 2 y = 4 and x + y = 4 . If m is the slope of its third side, then the sum, of all possible distinct values of m , is :

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TestHub · Accepted Answer

Slope of the third side = slope of the perpendicular bisector of given lines
$h : \frac{- x + 2 y - 4}{5} = \pm \frac{x + y - 4}{2}$
$h_{1} : 2 (- x + 2 y - 4) = 5 (x + y - 4) h_{2} : 2 (- x + 2 y - 4) = - 5 (x + y - 4) M_{L_{1}} : - [\frac{5 + 2}{5 - 2 2}] M_{L_{2}} : - [\frac{5 - 2}{5 + 2 2}] M_{L_{1}} + M_{L_{2}} = - [\frac{5 + 2}{5 - 2 2} + \frac{5 - 2}{5 + 2 2}]$
$= - [\frac{( 5 + 2 ) ( 5 + 2 2 ) + ( 5 - 2 ) ( 5 - 2 2 )}{- 3}] = 6$

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