Show that A(3, 2), B(0, 5), C(-3, 2) and D(0, -1) are the vertices of a square.
Given: The points are A(3, 2), B(0, 5), C(-3, 2) and D(0, -1).
Note: For a quadrilateral to be a square, all the sides of the quadrilateral must be equal in length and the diagonals must be equal in length as well.
AB
= 3√2 units
BC
= 3√2 units
CD
= 3√2 units
DA
= 3√2 units
Therefore, AB = BC = CD = DA …..(1)
AC
= 6 units
BD
= 6 units
Therefore, AC = BD …..(2)
From 1 and 2, we have all the sides of ABCD are equal and the diagonals are equal in length as well.
Therefore, ABCD is a square.
Hence, the points A, B, C and D are the vertices of a square.