Question

three vertices of a parallelogram,taken in order are (1,2),(0,4)and(3,7). find the fourth vertex

Answer 1

can be find by using distance formula
or

$|{x1 + x2 + x3 + x4 } \binom{?}{?} {y1 + y2 + y3 + y4} |$

Answer 2

from the line AB
coordinates of o ( x1+x2/2, y1+y2/2)
                           = ( 1+3/2     ,   2+7/2)
                           = ( 4/2      ,9/2)
                          =(2 ,9/2)
let the coordinate of fourth vertex be (x2,y2)
=from line AD
x=x1+x2/2                       y=y1+y2/2
2=0+x2/2                       9/2=4+y2/2 
2*2=x2                            (9/2*2)-4=y2
∴x2=4 and y2=5