Question

The equation of the three sides of a triangle are $x=2,y+1=0$ and $x+2y=4$. The coordinates of the circumcentre of the triangle are

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

Answer 1

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

Sides of the given triangle:

$x=2,y+1=0,x+2y=4$

Line $x=2$ will cut $x$-axis at $(2,0)$.

Line $y+1=0$ will cut $y$-axis at $(0,-1)$.

Line $x+2y=4$ will intersect with line $x=2$ in point $(2,1)$ i.e., $C(2,1)$

Line $x+2y=4$ will intersect line $y+1=0$ in point $(6,-1)$ i.e., $A(6,-1)$

Now,

For $△ABC$, midpoint of $AC$ is the circumcentre.

$\therefore$ circumcentre $=[\frac{(2+6)}{2},\frac{(1-1)}{2}]$

$\Rightarrow (4,0)$\

Hence the circumcentre of the triangle is $(4,0)$.