# Relations Problem 3

### General hints

Remember that we've defined the square root function to return (only) the non-negative
value.

### Hints for (a)

Let \(q = \sqrt{(x-a)^2 + (y-b)^2}\).
What is q geometrically?
Find a high-level name for q,
in terms of the points (x,y) and (a,b).

Try drawing a picture of two
circles with q, s, and r marked on the picture.
Draw a couple examples like this, until you have a hypothesis about
which circles are related and which ones aren't.

### Hints for (b)

Remember the standard outline for an antisymmetry proof: pick two objects,
suppose they are related in both directions, then try to show that they are
equal.