Given: The 4 points are A(2, -2), B(8, 4), C(5, 7) and D(-1, 1).

Note: For a quadrilateral to be a rectangle, the opposite sides of the quadrilateral must be equal and the diagonals must be equal as well.

AB

= 6√2 units …..(1)

BC

= 3√2 units …..(2)

CD

= 6√2 units …..(3)

AD

= 3√2 units …..(4)

From equations 1, 2, 3 and 4, we have

AB = CD and BC = AD …..(5)

Also, AC

= 3√10 units

BD

= 3√10 units

Thus, AC = BD …..(6)

From equations 5 and 6, we can conclude that the opposite sides of quadrilateral ABCD are equal and the diagonals of ABCD are equal as well.

Therefore, point A, B, C and D are the angular points of a rectangle.