A standard football field is 100 yards long and 53 1/3 yards wide. A quarterback is standing on the 25 yard line, 25 yards from the left sideline, throws the ball to a receiver who is on the 35 yard line, 5 yards from the right sideline, as shown in the figure.

(a) How long was the pass? [Hint: Place the field in the first quadrant of the coordinate plane, with the left sideline on the y-axis and the goal line behind the quarterback on the x-axis. What are the coordinates of the quarterback and the receiver?] (Round your answer to one decimal place.)

(b) A player is standing halfway between the quarterback and the receiver. What are his coordinates? (Round each answer to one decimal place.:

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  1. The receiver is 10 yd downfield and 53 1/3 - 25 - 5 = 23 1/3 yds to the right.

    So, the distance is clearly

    √(10^2 + (70/3)^2) yds

    QB: (25,25)
    Rcvr: (35,48 1/3)

    So, take their averages to find the midpoint.

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