Q16 of 77 Page 7

Prove that the points (3, - 2), (4, 0), (6, - 3) and (5, - 5) are the vertices of a parallelogram.

Given: Points (3, - 2), (4, 0), (6, - 3) and (5, - 5)


To prove: The points are vertices of parallelogram


Formula Used:


The distance between the points (x1,y1) and (x2,y2) is:


Distance


Explanation:


We know if the quadrilateral is parallelogram if opposite sides are equal.


Let our points be A (3, - 2), B(4, 0), C(6, - 3) and D(5, - 5).



For AB,


AB =



= √5 units


For BC,


BC =



units


For CD,


CD =



units


For AD,


AD =



= √13 units


Here, we observe that AB = CD and AD = BC, which means that the quadrilateral formed by lines joining by points, is parallelogram.


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