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 7x – y + 3 = 0 and x + y – 3 = 0
Solving 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 7x – y + 3 = 0 is 7
Slope of the line x + y – 3 = 0 is –1
Let slope of BC be m
Since ∆ABC is an isosceles triangle, ∠B = ∠C
⇒ 3m2 + 8m – 3 = 0 or m2 = –1
⇒ 3m2 + 9m – m – 3 = 0 (m2 = –1 is not possible for real value of m)
⇒ 3m (m + 3) –1 (m + 3) = 0
⇒ (m + 3) (3m – 1) = 0
Thus, equation of BC are 3x + y – 7 = 0 or x – 3y + 31 = 0
Hope! This will be helpful for you.
Cheers!!!