Can diagonal vectors prove that orthogonal diagonals create a square rectangle?

[kidia]

I have problem on this one:

Using vectors,show that if a diagonals of rectangle are orthogonal then the rectangle must be square.

 

[HallsofIvy]

Set up a coordinate system so that one corner of the rectangle is at the origin, the two sides are along the positive x and y axes. Then the corners of the rectangle are at (0,0), (w,0), (0,h), (w,h).

One of the diagonals, from (0,0) to (w,h) is given by the vector wi+ hj.
The other, from (w,0) to (0,h) is given by the vector -wi+ hj

If the two diagonals are orthogonal then their dot product must be 0.

What IS the dot product of wi+ hj and -wi+ hj?

What does that tell you about w and h?

 

[kidia]

super,thanx professor