Question

The intersection of three lines $x-y=0,x+2y=3$ and $2x+y=6$ is a

• A. Right angled triangle
• B. Equilateral triangle
• C. Isosceles triangle
• D. None of the above

Answer 1

Answer: (C)

$L_1:x-y=0$
$L_2:x+2y=3$
$L_3:x+y=6$
on solving $L_1$ and $L_2$
$y=L$ and $x=1$
$L_1$ and $L_3$ :
$y=2$
$L_2$ and $L_3$ :
$x+y=3$
$2x+y=6$
$x=3$
$y=0$
$AC=\sqrt{4+1}=\sqrt{5}$
$BC=\sqrt{4+1}=\sqrt{5}$
$AB=\sqrt{1+1}=\sqrt{2}$
so its an isosceles triangle