Because you (cleverly) chose to make A's initial position the origin of your coordinate system, A's position at t= 0 is, indeed, (0,0). Since A is moving due east (and you chose to make the positive x-axis that direction) at 8 km/h, A's position at time t hours is (8t, 0). Yep, that's what you got!
Initially, B was "5 km to the south east" so B's initial position is (5\frac{\sqrt{2}}{2}, 5\frac{\sqrt{2}}{2} (sin(45^o)= \frac{\sqrt{2}}{2}). Since B is moving straight North at 6 km/h, B's position at time t hours must be (5\frac{\sqrt{2}}{2}, 5\frac{\sqrt{2}}{2}+ 6t)). If 5\frac{\sqrt{2}}{2}= 3.53(and it is) you are correct. Glad you don't have to quit school!
Now what is the distance between those points? (Hint: since distance is always positive, minimizing distance is the same as mininizing distance squared- so you can ignore the square root in the distance formula.)
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