Question

The orthocentre of the triangle PAB is

• A. $(\frac{7}{5},\frac{25}{8})$
• B. $(\frac{8}{25},\frac{7}{5})$
• C. $(\frac{11}{5},\frac{8}{5})$
• D. $(5,\frac{8}{7})$

Answer 1

The correct option is C $(\frac{11}{5},\frac{8}{5})$


Equation of $AB$ is
$y-0=\frac{\frac{8}{5}}{-\frac{9}{5}-3}(x-3)=\frac{8}{-24}(x-3)$
$\Rightarrow y=-\frac{1}{3}(x-3)$
$\Rightarrow x+3y=3$ .. (i)
Equation of the straight line perpendicular to $AB$ through $P$ is $3x-y=5$
Equation of $PA$ is $x-3=0$
The equation of striaght line perpendicular to $PA$ through $B(\frac{-9}{5},\frac{8}{5})$ is $y=\frac{8}{5}$.
Hence the orthocentre is $(\frac{11}{5},\frac{8}{5})$