Question

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

The coordinates of G are

Answer 1

Coordinates of G =
`(2,0)`

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
`((a+c)/(2),(b+d)/(2))`

Diagonals of a parallelogram bisect each other.

So,

Midpoint of DF = Midpoint of EG

Midpoint of DF =
`((-4+3)/(2),(-2+3)/(2))=((-1)/(2),(1)/(2))`

Midpoint of EG =
`((-3+x)/(2),(1+y)/(2))`

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

Therefore,

`((-1)/(2),(1)/(2)) =((-3+x)/(2),(1+y)/(2))\\\\(-1)/(2)=(-3+x)/(2),\,(1)/(2)=(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)`