Four friends A, B, C and D are sitting in a park at points: A (3 , 4), B (6, 7), C (9, 4) and D (6, 1). Their sitting positions form

By distance formula, ^{$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$} $AB = \sqrt{(6-3)^2 +(7-4)^2} =\sqrt{9+9} = \sqrt{18}$_units $AB = \sqrt{(9-6)^2 +(4-7)^2} =\sqrt{9+9} = \sqrt{18}$_units $CD = \sqrt{(6-9)^2 +(1-4)^2} =\sqrt{9+9} = \sqrt{18}$_units $CD = \sqrt{(3-6)^2 +(4-1)^2} =\sqrt{9+9} = \sqrt{18}$_units AB = BC = CD = DA = ^{$\sqrt{18}$_units}

Also, AC = BD. So, its a square.