Question

If A(1,2), B(4,3), C(6,6) are the vertices of a parallelogram ABCD ,then find the coordinate of the fourth vertex.

Answer 1

Let the fourth vertex be (a, b)
O is the mid point of AC&BD
Mid point of AC is O{(1+6÷2),(2+6÷2)}
i.e.O(7/2,4)
Mid point of BD is O {(4+a÷2),(3+b÷2)}
4+a÷2=7/2
8+2a=14
2a=14-8
a=6/2
a=3
&3+b÷2=4
3+b=8
b=5
Hence, the fourth vertex of a parallelogram ABCD is D(3,5)