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:

  1. 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 $=(3, y)=3, \frac{3}{4}$



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