Question:
If a $\triangle A B C$ has vertices $A(-1,7), B(-7,1)$ and $C(5,-5)$, then its orthocentre has coordinates :
Correct Option: , 2
Solution:
$m_{B C}=\frac{6}{-12}=-\frac{1}{2}$
$\therefore$ Equation of AS is $y-7=2(x+1)$
$y=2 x+9$ ....(i)
$m_{A C}=\frac{12}{-6}=-2$
$\therefore$ Equation of $B P$ is $y-1=\frac{1}{2}(x+7)$
$y=\frac{x}{2}+\frac{9}{2}$ ...(ii)
From equs. (i) and (ii),
$2 x+9=\frac{x+9}{2}$
$\Rightarrow 4 x+18=x+9$
$\Rightarrow 3 x=9 \Rightarrow x=-3$
$\therefore y=3$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.