Question

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

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

Answer 1

Answer: (C)

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