Question

The orthocentre of the 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)

$(3,\frac{3}{4})$

To find orthocentre of the triangle formed by $(0,0),(3,4)$ and $(4,0)$
Let $H$ be the orthocenter of $△OAB$
Therefore $($slope of $OP$ i.e $OH).($slope of $BA)=-1$
$\Rightarrow \left(\frac{y-0}{3-0}\right).\left(\frac{4-0}{3-4}\right)=-1\Rightarrow -\frac{4}{3}y=-1\Rightarrow y=\frac{3}{4}$
Therefore required orthocenter $=(3,y)=(3,\frac{3}{4})$