Question

Equation of two equal sides of a triangle are the lines $7x-y+3=0$ and $x+y-3=0$ and the third side passes through the point $(1,-10)$, then the equation of the third side can be

• A. $x-3y=31$
• B. $3x+y+7=0$
• C. $x+3=0$
• D. $y=3$

Answer 1

Answer: (A), (B)

The correct options are
A $x-3y=31$
B $3x+y+7=0$

The equation of any line passing through $(1,-10)$ is $y+10=m(x-1)$

Since, it makes equal angles, say $\theta$, with the given lines,
therefore $\tan \theta =\frac{m-7}{1+7m}=\frac{m-(-1)}{1+m(-1)}\Rightarrow m=\frac{1}{3}$ or $-3$

Hence, the equation of third side are
$y+10=\frac{1}{3}(x-1)$ or $y+10=-3(x-1)$

$\Rightarrow x-3y-31=0$ or $3x+y+7=0$