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.