( 1999? Yantai) As shown in the figure, the quadrilateral AOBC is rectangular, the coordinates of point A are (0,3), the coordinates of point B are (4,0), and the moving points P and Q come out from p

( 1999? Yantai) As shown in the figure, the quadrilateral AOBC is rectangular, the coordinates of point A are (0,3), the coordinates of point B are (4,0), and the moving points P and Q come out from point O at the same time. (1) Let OQ=a, then OA+AP=3a,

OC=OA2+AC2=5，( 1)

∫AC∨OB，

∴△orq∽△crp(2 points)

∴OQPC=ORRC，

∴PC=32a，

∫OA+AC = 7, that is, 3a+32a=7,

∴ A = 149, (4 points)

AP=53, (5 points)

∴P point coordinates (53,3), Q point coordinates (149,0),

Let the functional relationship of the straight line PQ be y=kx+b,

∴ 53k+b = 3 149k+b = 0, and the solution is k = 27b =? Forty two.

Therefore, the functional relationship of the straight line PQ is y = 27x-42；; (8 points)

(2) When 0≤t≤ 157, point P is on OA and point Q is on OB.

S= 12×OQ×OP= 1225t2，

When 157≤t≤5, point P is on AC and point Q is on OB.

S = 12× OQ× BC = 65t, (4 points)

When 5 < t ≤ 70 1 1, points p and q are on BC.

S = 12× PQ× OB = 28-225t。 (6 points)