Question

Three vertices of a parallelogram taken in order are (1,2),(2,4),(3,7). Find it's fourth vertex

Answer 1

A = (1,2)
B = (2,4)
C = (3,7)
D = (a,b)

AC is a diagonal and BD is a diagonal (taken in order)
so, we know that the diagonals bisect each other in parallelogram...so the diagonals are divided in ratio 1:1

So, let that intersection point be O (X,Y)
considering diagonal AC, applying mid point theorem
X = 1+3/2 = 4/2 = 2
Y = 2+7/2 = 9/2

now, considering diagonal BD 
2 = 2+a/2 
4-2 = a
2 = a
and
9/2 = 4+b/2
9-4 = b
5 = b

therefore, the fourth vertex D = (2,5) 

Answer 2

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