Mathematics, 25.01.2021 19:50 Iyana678

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

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Answer from: Franklyn3834

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

Recall:

Diagonals of a parallelogram bisects each other, meaning they divide each other into equal parts.Midpoint formula = $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$

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:

midpoint of DF = midpoint of EG

Find midpoint of D(-4, - 2) and F(3, 3) using $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$ :

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

Find midpoint of E(-3, 1) and G(x, y) using $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$ :

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

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

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

Solve for x:

$\frac{-1}{2} = \frac{-3 + x}{2}$

Cross multiply

$2(-1) = 2(-3 + x)\\\\-2 = -6 + 2x\\\\-2 + 6 = 2x\\\\4 = 2x\\\\\mathbf{x = 2}$

Solve for y:

$\frac{1}{2} = \frac{1 + y}{2}$

Cross multiply

$2(1) = 2(1 + y)\\\\2 = 2 + 2y\\\\2 - 2 = 2y\\\\0 = 2y\\\\\mathbf{y = 0}$

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

Learn more about parallelogram on:

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Answer from: b00n4l1f3

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:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Two diagonals of the parallelogram DEFG are DF and EG.

$\text{Midpoint of DF}=\text{Midpoint of EG}$

$\left(\dfrac{-4+3}{2},\dfrac{-2+3}{2}\right)=\left(\dfrac{-3+a}{2},\dfrac{1+b}{2}\right)$

$\left(\dfrac{-1}{2},\dfrac{1}{2}\right)=\left(\dfrac{-3+a}{2},\dfrac{1+b}{2}\right)$

On comparing both sides, we get

$\dfrac{-3+a}{2}=-\dfrac{1}{2}$

-3+a=-1

a=-1+3

a=2

And,

$\dfrac{1+b}{2}=\dfrac{1}{2}$

1+b=1

b=1-1

b=0

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

Answer from: Quest

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step-by-step explanation:

Answer from: Quest

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