Another service from Omega

Problem 2



Show that if the diagonals of a rectangle intersect at right angles then, the rectangle is a square.

> a := vector([a1,a2]); b := s*vector([-a2,a1]);

                                a := [ a1, a2 ]

                              b := s [ - a2, a1 ]

Here the vectors "a" and "b" denote the sides of a general rectangle on the plane. The scalar "s" is the ratio of the lengths of the two sides. Here is the picture,
picture here

> diag1 := a+b: diag2 := a-b:

> solve( angle(diag1,diag2) = Pi/2, s);

                                     1, -1

so yes! it is a square.

Link to the commands in this file
Carlos Rodriguez <>
Last modified: Wed Oct 23 11:30:37 EDT 1996