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Answer:
The diagonals of the polygon ABCD bisect each other
Step-by-step explanation:
The given vertices of the polygon are;
A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1)
Given that the vertices of the polygon in clockwise order from the top left corner are ABCD, we have the diagonals as AC and DB
By the midpoint formula, we have;
Where;
= The midpoint coordinates
Therefore, the midpoint of diagonal AC =
The midpoint of diagonal DB =
Therefore, given that the coordinates of the location of the midpoint of the diagonals AC and DB is the same, the diagonals bisect each other
Each diagonal passes through the midpoint of the other diagonal.