Step-by-step explanation:
Since they want to prove that ABCD is a square, you only need to know the lengths of two adjacent sides.
Distance formula: d = [tex]\sqrt\\[/tex](x2 - x1)^2 + (y2 - y1)^2
A: (3, 4) B: (2, -2) C: (-4, -1) D: (-3, 5)
Distance of AB where A = (x1, y1) and B = (x2, y2)
d = [tex]\sqrt\\[/tex](2 - 3)^2 + (-2 - 4)^2
d = [tex]\sqrt\\[/tex](-1)^2 + (-6)^2
d = [tex]\sqrt\\[/tex]1 + 12
d = [tex]\sqrt\\[/tex]13
Distance of CB where B = (x1, y1) and C = (x2, y2)
d = [tex]\sqrt\\[/tex](-4 - 2)^2 + (-1 - (-2))^2
d = [tex]\sqrt\\[/tex](-6)^2 + (1)^2
d = [tex]\sqrt\\[/tex]12 + 1
d = [tex]\sqrt\\[/tex]13
Since dAB = dCB, therefore quadrilateral ABCD is a square.
