Question

The circumcenter of the triangle formed by the line $y=x,y=2xandy=3x+4is$

• A. $\left(6,8\right)$
• B. $(6,-8)$
• C. $(3,4)$
• D. $(-3,-4)$

Answer 1

The correct option is B $(6,-8)$

REF. Image.

Solving equations of lines simultaneously (taken 2 at a time)

we get

$A\equiv (-2,-2)B\equiv (-4,-8)C\equiv (0,0)$

$\to$ equation of $\perp$ bisector of AC

1. slope $\Rightarrow m.1=-1$

$\Rightarrow M=-1$

passes through (-1, -1)

$a+y=-2$

$\to$ equation of $\perp$ bisector of BC

1 slope $\Rightarrow m.2=-1$

$m=-1/2$

passes through (-2, -4)

$x+2y=-10$

solving $x+y=-2$ & $x+2y=-10$ simultaneously

we get cirumcenter $\equiv (6,-8)$