Question

Three vertices of parallelogram DEFG are D(-4,-2), E(-3,1) and F(3, 3). Find the coordinates of G.

Answer 1

Answer:

Coordinates of G = $(2,0)$

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 $(a,b),\,(c,d)$ are given by $(\frac{a+c}{2},\frac{b+d}{2})$

Diagonals of a parallelogram bisect each other.

So,

Midpoint of DF = Midpoint of EG

Midpoint of DF = $(\frac{-4+3}{2},\frac{-2+3}{2})=(\frac{-1}{2},\frac{1}{2})$

Midpoint of EG = $(\frac{-3+x}{2},\frac{1+y}{2})$

Let coordinates of G be $(x,y)$

Therefore,

$(\frac{-1}{2},\frac{1}{2}) =(\frac{-3+x}{2},\frac{1+y}{2})\\\\\frac{-1}{2}=\frac{-3+x}{2},\,\frac{1}{2}=\frac{1+y}{2}\\\\-1=-3+x,\,1=1+y\\\\x=-1+3,\,y=1-1\\x=2,\,y=0$

So,

Coordinates of G = $(2,0)$