Question

Show that straight lines $x+y=0,3x+y-4=0$ , $x+3y-4=0$ form isosceles

Answer 1

coordinates of A by intersection of $L_1,L_3$

$A(2,-2)$

coordinates of B by intersection of $L_1,L_2$

$B(-2,2)$

coordinates of C by intersection of $L_2,L_3$

$C(1,1)$

$AC=\sqrt{(2-1{)}^2+(-2-1{)}^2}=\sqrt{10}$

$BC=\sqrt{(-2-1{)}^2+(2-1{)}^2}=\sqrt{10}$

$AB=\sqrt{(2+2{)}^2+(-2-2{)}^2}=4\sqrt{2}$

$AC=BC$

Triangle is isosceles