Question

Orthocentre of triangle with vertices $(0,0),(3,4)$ and $(4,0)$ is

• A. $(3,\frac{5}{4})$
• B. $(3,12)$
• C. $(3,\frac{3}{4})$
• D. $(3,9)$

Answer 1

Answer: (C)

To find orthocentre of the triangle formed by $(0,0)(3,4)$ and $(4,0)$.

Let $H$ be the orthocentre of $\Delta OAB$
$\therefore$ (slope of $OP$ i.e. $OH$) -(slope of $BA)=-1$
$\Rightarrow \left(\frac{y-0}{3-0}\right).\left(\frac{4-0}{3-4}\right)=-1$
$\Rightarrow -\frac{4}{3}y=-1$
$\Rightarrow y=\frac{4}{3}$
$\therefore$ Required orthocentre $=(3,y)=(3,\frac{3}{4})$