∴OB=2,AB=m，
∴S△AOB= 12？ OB？ AB= 12×2×m= 12，
∴m= 12；
∴ The coordinate of point A is (2 12),
Substitute a (2, 12) into y=kx to get 12=k2.
∴k= 1；
(2)∵ When x= 1, y =1; When x=3, y= 13,
Inverse proportional function y =1x. When x > 0, y decreases with the increase of x,
∴ When 1≤x≤3, the value range of y is13 ≤ y ≤1;
(3) From the image, we can see that P and Q are symmetrical about the origin.
∴PQ=2OP，
The inverse ratio resolution function is y= 1x, let P(a, 1a),
∴OP=a2+( 1a)2=(a？ 1a)2+2，
The minimum value of op is 2,
The minimum PQ length of a line segment is 22.