(1) Let A(x_{1}, y_{1}) and B(x_{2} , y_{2}) be the given points

By distance formula d(A,B) = √[(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}]

Here x_{1} = 2, y_{1} = 3 , x_{2} = 4, y_{2} = 1

d(A,B) = √[(4-2)^{2}+(1-3)^{2}]

= √[2^{2}+(-2)^{2}]

= √8

= 2√2

Hence the distance between A and B is 2√2 units.

(2) Let P(x_{1}, y_{1}) and Q(x_{2} , y_{2}) be the given points

By distance formula d(P,Q) = √[(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}]

Here x_{1} = -5, y_{1} = 7 , x_{2} = -1, y_{2} = 3

d(A,B) = √[(-1-(-5))^{2}+(3-7)^{2}]

= √[4^{2}+(-4)^{2}]

= √32

= 4√2

Hence the distance between P and Q is 4√2 units.

(3) Let R(x_{1}, y_{1}) and S(x_{2} , y_{2}) be the given points

By distance formula d(R,S) = √[(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}]

Here x_{1} = 0, y_{1} = -3 , x_{2} = 0, y_{2} = 5/2

d(A,B) = √[(0-0)^{2}+((5/2) -(-3))^{2}]

= √[0^{2}+(11/2)^{2}]

= √(121/4)

= 11/2

Hence the distance between P and Q is 11/2 units.