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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.
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.