If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.

Let three vertices be A(1, -2), B(3, 6) and C(5, 10) and fourth vertex be D(x, y)


It is given that quadrilateral joining these four vertices is parallelogram, ie □ABCD is parallelogram.


We know that diagonals of parallelogram bisect each other, ie midpoint of the diagonals coincide.



Let E(xm , ym) be the midpoint of diagonals AC and BD.


By midpoint formula,


x = , y =


For diagonal AC,


xm = , ym =


xm = , ym =


E(xm , ym) ≡ (3, 4)


For diagonal BD,


3 = , 4 =


x = 6 – 3 , y = 8 – 6


x = 3 and y = 2


Hence, our fourth vertex is D(3 , 2)


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