Question

If equation of three sides of a triangle are $x=2$, $y+1=0$ and $x+2y=4$ then co-ordinates of circumcentre of this triangle are?

• A. $(4,0)$
• B. $(2,-1)$
• C. $(0,4)$
• D. $(-1,2)$

Answer 1

The correct option is A $(4,0)$

$Formulaused$
$midpo\mathrm{int}formula=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
$equationoflinepas\sin gthroughtwopo\mathrm{int}s$
$y-y_1=m(x-x_1)$
$Given$
$x=2.........\left(i\right)$
$y=-1..........\left(ii\right)$
$x+2y=4...........\left(iii\right)$
$from\left(i\right)and\left(ii\right)$
$A(2,-1)$
$from\left(ii\right)and\left(iii\right)$
$B(6,-1)$
$from\left(i\right)and\left(iii\right)$
$C(2,1)$
$LetD,E,Fbethemidpo\mathrm{int}sofAB,BCandCArespectively$
$D(4,-1)$
$E(4,0)$
$F(2,0)$
$Slopeof$
$\left(i\right)=0$
$\left(ii\right)=0$
$\left(iii\right)=-1/2$
$Slopeoflineperpendiculatto$
$\left(i\right)=-1/0$
$\left(ii\right)=-1/0$
$\left(iii\right)=2$
$Equationofline$
$DO$
$(y-0)=\frac{-1}{0}(x-4)$
$\Rightarrow x=4.......\left(iv\right)$
$SimilarlyequationofFO$
$y+=0.........\left(v\right)$
$Solving\left(iv\right)and\left(v\right)$
$O(4,0)$