Show that the points A(5, 6), B (1, 5), C(2, 1) and D(6, 2) are the vertices of a square.

Vertices of a quadrilateral are A(5,6), B(1,5), C(2,1) and D(6,2).

Using distance formula =

AB = = = units

BC = = = units

CD = = = units

DA = = = units

AB = BC = CD = DA

BD = = = units

AC = = = units

All the four sides of the quadrilateral are equal and diagonals are of equal length. Therefore, the given vertices form a square.