P is 300 km eastward of O and Q is 400 km north of O. R is exactly in the middle of Q and P. The distance between Q and R is

Place O at (0,0), P at (300,0) and Q at (0,400). The midpoint R of P(300,0) and Q(0,400) is R=(150,200), as computed using the midpoint formula . Using the distance formula between Q(0,400) and R(150,200) gives sqrt((150-0)^2 + (200-400)^2) = sqrt(22500 + 40000) = sqrt(62500) = 250 km . Equivalently, PQ is the hypotenuse of a 3-4-5 right triangle with length 500 km, and R being the midpoint makes QR half of that, i.e., 250 km . Thus option 1 (250 km) is correct.