Straight Line And Pair Of Straight Lines Ques 66
- 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)
Show Answer
Answer:
66.$7x-4y+25=0,4x+7y=11=0,7x-3=0$
Solution:
Formula:
Equation Of Lines Parallel And Perpendicular To A Given Line :
- Let the coordinates of third vertex be $C(a, b)$.
Since, $C H$ is $\perp A B$,
$$ \begin{aligned} & \therefore \quad \frac{b}{a} = \frac{4}{-7} = -1 \\ & \Rightarrow \quad 4 b=7 a \end{aligned} $$
Also, $A H \perp B C$
$$ \begin{alignedat} & \therefore \quad-\frac{1}{5} \quad \frac{3-b}{-2-a}=-1 \\ & \Rightarrow \quad 3-b=-10-5 a \end{aligned} $$
On solving Eqs. (i) and (ii), we get
$$ a=-4, b=-7 $$
BETA
