Question 7.

7. Equation of two equal sides of a triangle are the lines 7x + 3y - 20 = 0 and 3x + 7y - 20 = 0  and third side passes through the point (-3,3) then the equation of third side can be-
(A) x + y = 0
(B) x - y + 6 = 0
(C) x + 3 = 0
(D)  y = 3

Dear student
Let ABC be isosceles triangle such that AB=ACLet AB and BC are given by7x+3y-20=0     ...(1)3x+7y-20=0       ....(2)Slope of (1) line=-73Slope of (2) line=-37Let m be the slope of BC, thentanABC=tanθtanθ=-73-m1-73m=-7-3m3-7mAlso, tanACB=tanθ=-37-m1-37m=-3-7m7-3m-7-3m3-7m=-3-7m7-3m-7+3m3-7m=-3+7m7-3m-7+3m7-3m=-3+7m3-7m49-9m2=9-49m240=-40m2-m2=1-m=±1m=1The equation of third side passing through (-3,3) having slope -1 or 1.y-3=-1x+3y-3=-x-3x+y=0or y-3=1x+3y-3=x+3x-y+6=0
So, the correct options are A and B.

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apply tan thita = mod of m2-m1/1+m1m2
for both equation and equate them     we know one slope , angle thita must be same since two sides are equal so apply the formula for both and then equate.

we will get a quadratic in another slope but there are four possible values since there is a mod and solve
solve 2 quadratics, in one u will get complex no.s
and in another u will get 1, -1.

just check options where 1, and -1 are the slopes and also check if (-3,3 ) satisfies this equation or not
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