The orthocentre of the triangle formed by lines $x+y+1=0 ; x-y-1=0$ and $3 x+4 y+5=0$ is

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Aicharya · Accepted Answer

$\begin{aligned} & x+y+1=0 ...(i)\ & x-y-1=0 ....(ii)\ & 3 x+4 y+5=0 ....(iii) \end{aligned}$ Slope of (i) is -1 Slope of (ii) is 1 $	herefore$ Triangle is right angled triangle and orthocentre of right angled triangle is the vertex where triangle has right angle. Solving (i) and (ii) $(x, y)=(0,-1) \Rightarrow 	ext { Orthocentre }$

The orthocentre of the triangle formed by lines $x+y+1=0 ; x-y-1=0$ and $3 x+4 y+5=0$ is

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