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  • Two equal sides of an isosceles triangle have the equations 7x – y + 3 = 0 and x + y = 3 and its third side passes through the point (-2, –1). Then the equation of the third side.<

Two equal sides of an isosceles triangle have the equations 7x – y + 3 = 0 and x + y = 3 and its third side passes through the point (-2, –1). Then the equation of the third side.

Option: 1

x=y-1


Option: 2

x=3y+1


Option: 3

4x+y+9=0


Option: 4

Both (B) and (C)


Answers (1)

 

 

Line Equally Inclined with two lines -

Line Equally Inclined with two lines

If the two lines with slope m1 and m2 are equally inclined to a line having slope m, then 

Two lines with slope m1 and m2 intersect at point A

 

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Let Equation of AB is 7x – y + 3 = 0 and equation of AC x + y = 3

Slope of AB = 7 and Slope of AC = -1

Let the equation of third side BC, = y = mx + c

Angle between AB and BC = Angle between AC and BC

\\\left | \frac{7-m}{1+7m} \right |=\left | \frac{-1-m}{1-m} \right |\\-6 m^{2}-16 m+6=0\\3m^2+8m-3=0\\m=-3\;\;and\;\;\;m=1/3\\equation \;\;of\;BC\;\;is\;\;\\(y-(-1))=-3(x-(-2))\Rightarrow 3x+y+7=0\\ or\\\left(y-\left(-1\right)\right)=\frac{1}{3}\left(x-\left(-2\right)\right)\Rightarrow x-3y=1

Posted by

Sumit Saini

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