Straight Line and Pair of Straight Lines 1 Question 26
26. Orthocentre of triangle with vertices $(0,0),(3,4)$ and $(4,0)$ is
$(2003,2 M)$
(a) $3, \frac{5}{4}$
(b) $(3,12)$
(c) $3, \frac{3}{4}$
(d) $(3,9)$
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Solution:
- To find orthocentre of the triangle formed by $(0,0)(3,4)$ and $(4,0)$.
Let $H$ be the orthocentre of $\triangle O A B$
$\therefore \quad$ (slope of $O P$ i.e. $O H$ ) (slope of $B A$ ) $=-1$
$$ \begin{aligned} \Rightarrow & & \frac{y-0}{3-0} \cdot \frac{4-0}{3-4} & =-1 \\ \Rightarrow & & -\frac{4}{3} y & =-1 \\ \Rightarrow & & y & =\frac{3}{4} \end{aligned} $$
$\therefore \quad$ Required orthocentre $=(3, y)=3, \frac{3}{4}$
