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.
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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.
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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.