Concept guide
Euclidean distance formula: computing, rejecting the negative root and comparing by squares
In one equal-unit orthonormal Cartesian frame let P=(1,2), Q=(4,6) and R=(6,−1). Find d(P,Q) and explain why the candidate −5 is not a distance; find the exact form of d(P,R) and decide that it is not an integer; compare d(P,Q) with d(P,R) through their squares; finally check that coincident points have distance zero and that the distance does not depend on the order in which the two points are written.