Let A(a, b), B(3,4) and C(-6,-8) respectively denote the centroid, circumcentre and orthoc…

Question

Let $A(a, b), B(3,4)$ and $C(-6,-8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P(2 a+3,7 b+5)$ from the line $2 x+3 y-4=0$

Accepted Answer

$A(a,b),\, B(3,4),\, C(-6,-8)$

$\Rightarrow a=0,b=0\, \Rightarrow P(3,5)$

Distance from $P$ measured along $x-2y-1=0$

$\Rightarrow x=3+r\cos 	heta ,\, y=5+r\sin 	heta $

$\begin{gathered} 	an 	heta =\frac{1}{2} \ r(2\cos 	heta +3\sin 	heta )=-17 \ \Rightarrow r=|\frac{-17\sqrt{5}}{7}|=\frac{17\sqrt{5}}{7} \end{gathered}$

Solutions · 1