Q5 of 149 Page 14

Three consecutive vertices of a parallelogram are (-2, -1), (1, 0) and (4, 3). Find the fourth vertex

Let three vertices be A(-2, -1), B(1, 0) and C(4, 3) and fourth vertex be D(x, y)



It is given that quadrilateral joining these four vertices is parallelogram.


∴□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) ≡ (1, 1)


For diagonal BD,


1 = , 1 =


∴ x = 2 – 1 , y = 2 – 0


∴ x = 1 and y = 2


Hence, our fourth vertex is D(1, 2)


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