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

The coordinates of vertex G of parallelogram DEFG is: (2, 0).

Recall:

The given vertices of parallelogram DEFG are:

D(-4, - 2), E(-3, 1) and F(3, 3)

Let (x, y) = coordinates of vertex G.

DF and EG are diagonals of parallelogram DEFG, therefore:

Find midpoint of D(-4, - 2) and F(3, 3) using  :

Find midpoint of E(-3, 1) and G(x, y) using  :

Make the midpoint of DF equal to the midpoint of EG, then solve for x and y.

Therefore, the coordinates of vertex G of parallelogram DEFG is: (2, 0).

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Given:

The three vertices of parallelogram DEFG are D(-4, - 2), E(-3, 1) and F(3, 3).

To find:

The coordinates of vertex G.

Solution:

Let the coordinates of vertex G are (a,b).

We know that, diagonal of parallelogram bisect equal other. It means, the midpoints of both diagonals are same.

Midpoint formula:

Two diagonals of the parallelogram DEFG are DF and EG.

On comparing both sides, we get

And,

Therefore, the coordinates of vertex G are (2,0).

1 and 2

step-by-step explanation:

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