Among the statements (S 1) : If A(5,-1) and B(-2,3) are two vertices of a triangle, whose …

Question

Among the statements
$(S 1)$ : If $A(5,-1)$ and $B(-2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, then its third vertex is $(-4,-7)$
and
(S2) : If positive numbers $2 a, b, c$ are three consecutive terms of an A.P., th...

Accepted Answer

$\begin{gathered} {m}_{AO}{m}_{BC}=-1 \end{gathered}$

$\begin{gathered} \Rightarrow 2h-3k=13\ldots \ldots \ {m}_{AB}{m}_{OC}=-1 \ \Rightarrow 4k=7h\ldots \ldots \ldots \ldots . \end{gathered}$

\Rightarrow  third vertex is $(-4,-7)$

Solution of statement -2

$\begin{gathered} 2a,b,c	o A\cdot P \ b=\frac{2a+c}{2}\Rightarrow 2a-2b+c=0 \end{gathered}$

herefore  lines $ax+by+c=0$ are concurrent then

$\begin{gathered} \frac{x}{2}=\frac{y}{-2}=\frac{1}{1} \ x=2y=-2 \end{gathered}$

$	herefore Pt$. Of concurrency is $(2,-2)$

herefore  Statement 2 is correct.

Solutions · 1