two sides of an isocesle triangle are given by the equation 7x-y+3=0 and x+y-3=0. if its third side passes through the point (1,-10) then its equations are-

Hi!

Here is the answer to your query.

Let ∆ABC be isosceles triangle with AB = AC

Let the equation of the sides AB and AC of the isosceles triangle ABC are 7

*x*–*y*+ 3 = 0 and*x*+*y*– 3 = 0Solving these two equations, we obtain the coordinate of vertex A as (0, 3). Now, BC passes through the point (1, –10)

Slope of the line 7

*x*–*y*+ 3 = 0 is 7Slope of the line

*x*+*y*– 3 = 0 is –1Let slope of BC be

*m*Since ∆ABC is an isosceles triangle, ∠B = ∠C

⇒ 3

*m*^{2}+ 8*m*– 3 = 0 or*m*^{2}= –1⇒ 3

*m*^{2}+ 9*m*–*m*– 3 = 0 (*m*^{2}= –1 is not possible for real value of*m*)⇒ 3

*m*(*m*+ 3) –1 (*m*+ 3) = 0⇒ (

*m*+ 3) (3*m*– 1) = 0Thus, equation of BC are 3

*x*+*y*– 7 = 0 or*x*– 3*y*+ 31 = 0Hope! This will be helpful for you.

Cheers!!!

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