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PLEASE HELP! MEDAL WILL BE AWARDED! The vertices of a quadrilateral, OABC, are (0,0), (4,2), (6,10) and (2,8) respectively. Use a vector method to answer the questions which follow. a. (i) State two geometrical relationships between the line segments OA and CB. (ii) Explain why OABC is a parallelogram b. If M is the midpoint of the diagonal OB, and N is the midpoint of the diagonal AC, determine the position vector of: (i) OM (ii) ON Hence, state one conclusion which can be made about the diagonals of the parallelogram.

Mathematics
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for a, OA and CB are pararell and has the same length. Because their "directional" vector is (6,10)-(2,8)=4,2 and (4,2)-(0,0)=4,2 and the length is from SQRT((6-2)^2+(10-8)^2)=Sqrt(20) and SQRT((4-0)^2+(2-0)^2)=Sqrt(20). Other sides are also paralell so its a paralellogramm for b, OM=OB/2=(6,10)/2=(3,5), same for ON. So the statement is that OM and ON are equal. The midpoints are in the same place.

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