Question

The centroid of the triangle formed by the lines $x+y=0:2x+y+5=0$ and $x-y=2$ is

• A. $(-7/3,11/3)$
• B. $(1,-1)$
• C. $(1,1)$
• D. $(3,1)$

Answer 1

The correct option is A $(-7/3,11/3)$

We have,

$x+y=0......\left(1\right)$

$2x+y+5=0.....\left(2\right)$

$x-y=2......\left(3\right)$

From equation (1) and (2) to,

$x+y=0$

$2x+y=-5$

On subtracting and we get,

$(x_1,y_1)=(-5,5)$

From equation (2) and (3) to, we get,

$2x+y+5=0$

$x-y-2=0$

On adding and we get,

$(x_2,y_2)=(-1,-3)$

From equation (3) and (1) to, and we get,

$x-y-2=0$

$x+y=0$

On adding and we get,

$(x_3,y_3)=(1,-1)$

For orthocenter and we get,

$(x,y)=\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}$

$(x,y)=(\frac{-5-1+1}{3},\frac{5-3-1}{3})$

$(x,y)=(\frac{-7}{3},\frac{11}{3})$

Hence, this is the answer.