Question

Show that the points A(1, 2), B(5, 4), C(3, 5) and D(-1, 5) are the vertices of a square.

Answer 1

$AB=\sqrt{(5-1{)}^2+(4-2{)}^2}=\sqrt{4^2+2^2}$

$BC=\sqrt{(3-5{)}^2+(5-4{)}^2}=\sqrt{2^2+1^2}$

$CD=\sqrt{(-1-3{)}^2+(5-5{)}^2}=\sqrt{4^2+0^2}$

$DA=\sqrt{(1+1{)}^2+(2-5{)}^2}=\sqrt{2^2+3^2}$

Since $AB\ne BC\ne CD\ne DA$

$\therefore$ It is not a square.