Question

three vertices of parallelogram are (1,2) (2,4) (3,7) find fourth vertex

Answer 1

we know, diagonals of parallelogram is intersected at midpoint of it.
that is, midpoint of each diagonal is same .
          see attachement
o is the intersection point of two diagonals
Let A (1,2) ,B(2,4), C(3,7) and D(x,y)
then, for x- co-ordinate
(1+3)/2 = (2+x)/4
4 = 2 + x
x = 2

for y- co-ordinate
(2+7)/2 = (4 +y)/2
9 = 4 + y
y = 5

hence, fourth vertex is D(x,y) = (2,5)