Q25 of 184 Page 10

Prove that the points (-2,-1), (1,0),(4,3) and (1,2) are the vertices of a parallelogram.

Note that to show that a quadrilateral is a parallelogram, it is sufficient to show that the diagonals of the quadrilateral bisect each other.



Let A(-2, -1), B(1, 0), C(4, 3) and D(1, 2) are the vertices of a parallelogram.


Let M be the midpoint of AC, then the coordinates of M are given by



Let N be the midpoint of BD, then the coordinates of N are given by



Thus, AC and BD have the same midpoint.


In other words, AC and BD bisect each other.


Hence, ABCD is a parallelogram.


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