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To prove:

The points (2, -1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram

To find:

The angle between diagonals of parallelogram.

Assuming:

A(2, 1), B(0, 2), C(2, 3) and D(4, 0) be the vertices.

Explanation:

Slope of AB Slope of BC Slope of CD Slope of DA Thus, AB is parallel to CD and BC is parallel to DA.

Therefore, the given points are the vertices of a parallelogram.

Now, let us find the angle between the diagonals AC and BD.

Let m1 and m2 be the slopes of AC and BD, respectively.  Thus, the diagonal AC is parallel to the y-axis.

∴∠ODB In triangle MND,

DMN Hence proved, the acute angle between the diagonal is .

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