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Sagot :

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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.

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