Straight Line and Pair of Straight Lines 1 Question 68
68. Two vertices of a triangle are $(5,-1)$ and $(-2,3)$. If the orthocentre of the triangle is the origin, find the coordinates of the third vertex.
(1978, 3M)
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Answer:
Correct Answer: 68. $7 x-4 y+25=0,4 x+7 y=11=0,7 x-4 y-3=0$
Solution:
- Let the coordinates of third vertex be $C(a, b)$.
Since, $C H$ is $\perp A B$,
$$ \begin{aligned} & \therefore \quad \frac{b}{a} \quad \frac{4}{-7}=-1 \\ & \Rightarrow \quad 4 b=7 a \end{aligned} $$
Also, $A H \perp B C$
$$ \begin{aligned} & \therefore \quad-\frac{1}{5} \quad \frac{3-b}{-2-a}=-1 \\ & \Rightarrow \quad 3-b=-10-5 a \end{aligned} $$
On solving Eqs. (i) and (ii), we get
$$ a=-4, b=-7 $$
