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In the diagram below, parallelogram ABCD has vertices A(1,3),
B(5,7), C(10,7), and D(6,3). Diagonals AC and BD intersect at E.
(Not drawn to scale)
What are the coordinates of point E?
(1) (0.5,2)
(3) (5.5,5)
(2) (4.5,2)
(4) (7.5,7)

Respuesta :

Answer:E(5,5;5)

E is midpoint of A and C, B and D

The coordinates of point E are (5.5, 5). Since the diagonals of the given parallelogram bisect each other at point E, it is said to be the midpoint of each diagonal.

Parallelogram:

  • A parallelogram is a quadrilateral that has 2 pairs of parallel sides.
  • In a parallelogram, the diagonals bisect each other at a common point called the point of intersection.
  • It is calculated by diving the length of any of the diagonal into two equal parts or
  • It is calculated by taking the averages of the coordinates of two vertices of the diagonal
  • That is, point of intersection = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Given parallelogram:

Given parallelogram ABCD has 4 vertices that are A(1,3), B(5,7), C(10,7), and D(6,3)

Diagonals AC and BD intersect at E.

So, E is the midpoint of AC or BD

Calculating the coordinates of point E:

Point E is the midpoint of AC or BD

So,

If we take the A and C vertices,

Coordinates of point E = [tex](\frac{1+10}{2},\frac{3+7}{2})[/tex]

                                      = [tex](\frac{11}{2} ,\frac{10}{2} )[/tex]

                                      = (5.5, 5)

If we take the B and D vertices,

Coordinates of point E = [tex](\frac{5+6}{2},\frac{7+3}{2})[/tex]

                                      = [tex](\frac{11}{2} ,\frac{10}{2} )[/tex]

                                      = (5.5, 5)

Therefore, the point of intersection is at E and the coordinates of point E are (5.5, 5).

Learn more parallelogram here:

https://brainly.com/question/11874218

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