Respuesta :
Answer:
Coordinates of G = [tex](2,0)[/tex]
Step-by-step explanation:
Given: Three vertices of parallelogram DEFG are D(-4,-2), E(-3,1) and F(3, 3).
To find: coordinates of G
Solution:
Midpoints of a side joining points [tex](a,b),\,(c,d)[/tex] are given by [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
Diagonals of a parallelogram bisect each other.
So,
Midpoint of DF = Midpoint of EG
Midpoint of DF = [tex](\frac{-4+3}{2},\frac{-2+3}{2})=(\frac{-1}{2},\frac{1}{2})[/tex]
Midpoint of EG = [tex](\frac{-3+x}{2},\frac{1+y}{2})[/tex]
Let coordinates of G be [tex](x,y)[/tex]
Therefore,
[tex](\frac{-1}{2},\frac{1}{2}) =(\frac{-3+x}{2},\frac{1+y}{2})\\\\\frac{-1}{2}=\frac{-3+x}{2},\,\frac{1}{2}=\frac{1+y}{2}\\\\-1=-3+x,\,1=1+y\\\\x=-1+3,\,y=1-1\\x=2,\,y=0[/tex]
So,
Coordinates of G = [tex](2,0)[/tex]
