Question

The equations of two equal sides of an isosceles triangle are 7x – y + 3 = 0 and x + y –3 = 0 and the third side passes through the point (1, -10). The equation of the third side is

• A. x – 3y – 31 = 0 but not 3x + y + 7 = 0
• B. 3x + y + 7 = 0 but not x – 3y – 31 = 0
• C. 3x + y + 7 = 0 or x – 3y – 31 = 0
• D. Neither 3x + y + 7 nor x – 3y – 31 = 0

Answer 1

The correct option is C 3x + y + 7 = 0 or x – 3y – 31 = 0

Any line through (1, - 10) is given by y + 10 = m(x - 1)
Since it makes equal angle ${}^{\prime }{\alpha }^{\prime }$ with the given lines 7x – y + 3 = 0 and x + y – 3 = 0, therefore
$tan\alpha =\frac{m-7}{1+7m}=\frac{m+1}{1+m(-1)}\Rightarrow m=\frac{1}{3}or-3$
Hence the two possible equations of third side are 3x + y + 7 = 0 and x - 3y - 31 = 0.