Question

Show that the following points form an isosceles triangle.

(-2, 0), (4, 0) and (1, 3)

Answer 1

To form isosceles Triangle Two sides most be equal

Consider $A(x_1,y_1)B(x_2,y_2)C(x_3,y_3)$

$AB=BC$ (may be isosceles)

$AB=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

So in our case

$A(-2,0),B(4,0)$ and $C(1,3)$

$AB=\sqrt{(4-(-2){)}^2+0^2}$

$=6$

$BC=\sqrt{(7-4{)}^2+(3{)}^2}=\sqrt{18}$

$CA=\sqrt{(3{)}^2+(3{)}^2}+\sqrt{18}$

$BC=CA$ Hence it is isoceles $△$