Question

Three vertices of parallelogram DEFG are
D(0, 2), E(-1, 5), and G (4, 0). Find
the coordinates of F.

Answer 1

Answer:

F(3,3)

Step-by-step explanation:

Answer 2

The coordinate of F is (3, 3).

Given

Three vertices of parallelogram DEFG are D(0, 2), E(-1, 5), and G (4, 0).

What is the formula to find the midpoints?

Diagonals of a parallelogram bisect each other, meaning they divide each other into equal parts.

The formula is used to find the midpoints are as follows;

$\rm \dfrac{x_1+x_2}{2} , \ \dfrac{y_1+y_2}{2}$

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

DF and EG are diagonals of parallelogram DEFG, therefore:

The midpoint of DF = midpoint of EG

Then,

The midpoint of D(0, 2) and F(x, y) is;

$\rm \dfrac{x_1+x_2}{2} , \ \dfrac{y_1+y_2}{2}\\\\\dfrac{0+x}{2}, \ \dfrac{2+y}{2}$

The midpoint of E(-1, 5) and G(4, 0) is;

$\rm \dfrac{x_1+x_2}{2} , \ \dfrac{y_1+y_2}{2}\\\\\rm \dfrac{-1+4}{2} , \ \dfrac{5+0}{2}\\\\\dfrac{3}{2}, \dfrac{5}{2}$

Comparing the equation;

$\rm \dfrac{0+x}{2} = \dfrac{3}{2}\\\\\dfrac{x}{2} = \dfrac{3}{2}\\\\x=3$

$\rm \dfrac{2+y}{2} =\dfrac{5}{2}\\\\2+y =5\\\\y = 5-2\\\\y =3$

Hence, the coordinate of F is (3, 3).

To know more about Midpoints click the link given below.

https://brainly.com/question/2994861