the mdpoints of the sides of a triangle are 3,4 4,6 5,7 find the coordinates of the vertices

The mdpoints of the sides of a triangle are  given as 3,4 4,6 5,7  since you have not separated them in brackets

we are assuming them to be (3,4),(4,6),(5,7)

Let the vertices of triangle be (x1,y1) (x2,y2),(x3,y3)

x1+x2=6    y1+y2=8      (i)

x2+x3=8   y2+y3=12    (ii)
x3+x1=10    y 3+y1=14  (iii)

Now From (i) x2=6-x1  using  this in (ii) we get  x3-x1 = 2  adding  this and (iii) x3 =6  x1=4 and x2 =2

Similarly solve the y equations to get y3=9 y1=5 and y2= 3