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5 marksVector Geometry Problems

CSEC Mathematics · January 2006 · Paper 2 · Question 13(d)

Using a vector method, determine the position vector of G, the midpoint of the line AC. Hence, state the coordinates of the point of intersection of the diagonals AC and BD of parallelogram ABCD.

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Other parts of this question

  1. 13(a)(i)Express in the form (x, y) the position vectors OA, OB, OC, and OD where O is the origin (0, 0).[2 marks]
  2. 13(a)(ii)Express in the form (x, y) the vectors AB and DC.[2 marks]
  3. 13(b)Calculate |AB| and hence determine the unit vector in the direction of AB.[2 marks]
  4. 13(c)(i)Using the answers in (a) (ii), state TWO geometrical relationships between the line segments AB and DC.[2 marks]
  5. 13(c)(ii)Explain why ABCD is a parallelogram.[2 marks]

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