Question

show that the diagonals of the quadrilateral formed by the vertices (-1, 2), (5, 4) ,(3, 4) and (-3,2) taken in order, bisect each other​

Answer 1

Step-by-step explanation:

the diagonals of the quadrilateral are bisect at the point (1,3 )

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Answer 2

The diagonals bisect each other.

Step-by-step explanation:

Let the quadrilateral be ABCD with coordinates of the vertices A(-1,2), B(5,4), C(3,4) and D(-3,2).

The coordinates of the midpoint of the diagonal AC will be = $(\frac{- 1 + 3}{2},\frac{2 + 4}{2}) = (1,3)$

And the coordinates of the midpoint of the diagonal BD will be = $(\frac{5 - 3}{2}, \frac{4 + 2}{2}) = (1,3)$

Therefore, the common point of diagonals AC and BD are (1,3) and hence it is the point of intersection of the diagonals AC and BD and it is the midpoint of them.

Hence, the diagonals bisect each other. (Proved)