Question

Orthocentre of a 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

The correct option is C $(3,\frac{3}{4})$

We know that orthocentre is the meeting point of altitudes of a $\Delta .$





Equation of altitude AD
$\Rightarrow$ AD line is parallel to Y - axis through (3,4)
$\Rightarrow x=3$ ~~~~~~~~~~~~~~(1)
Similarly $e{q}^{n}ofOEis$
y = - $\frac{3-4}{4-0}x$
$\Rightarrow y=x/4$ ~~~~~~~~~~~~~~~(2)
Solving (1) and (2), we get orthocentre as (3,3/4).