Here is the diagram showing the four points $A$, $B$, $C$, and $D$ forming a square. The lines drawn between opposite points demonstrate the perpendicular relationship as described.

If you have any further questions or would like more details, feel free to ask!

Here are some related questions for further exploration:

1. What are the properties of the diagonals in a square?
2. How would the diagram change if the shape were a rhombus instead of a square?
3. Can you explain why the diagonals in this configuration are perpendicular?
4. What are the coordinates of the points if the square is centered at the origin?
5. How do the angles between the lines change if the shape is altered to a rectangle?

Tip: In a square, the diagonals are always equal in length and bisect each other at right angles.