Q. 104.6( 5 Votes )

Two sides of an isosceles triangle are given by the equations 7x – y + 3 = 0 and x + y – 3 = 0 and its third side passes through the point (1, -10). Determine the equation of the third side.

Answer :

Given: two side of an isosceles triangle are 7x – y + 3 = 0 and x + y – 3 = 0 and its third side passes through the point (1, -10)


To find: third side of isosceles triangle


Explanation:


Let ABC be the isosceles triangle, where 7x y + 3 = 0 and x + y 3 = 0 represent the sides AB and AC, respectively.
Let AB = BC


Diagram:



AB = BC


tan B = tan C


Here,


Slope of AB = 7


Slope of AC = 1


Let m be the slope of BC.


Then,



Taking the positive sign, we get:


m2 – 8m + 7 = 7m2 + 8m + 1




Now, taking the negative sign, we get:


(m – 7) (m – 1) = - (7m + 1)(m + 1)


m2 – 8m + 7 = - 7m2 – 8m – 1


m2 = - 1 (not possible)


Equations of the third side is


y + 10 = - 3(x – 1) and


3x + y + 7 = 0 and x – 3y – 31 = 0


Hence, third side of isosceles triangle is 3x + y + 7 = 0 and x – 3y – 31 = 0


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