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Prove that points (-3, -1), (2, -1), (1, 1) and (-2, 1) taken in order are the vertices of a trapezium.

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Given: Points of the quadrilatreral A(-3, -1), B(2, -1), C(1, 1), and D(-2, 1).

To Prove: ABCD is a trapezium

Proof:

For proving ABCD to be a trapezium, we need to prove that two of the sides are parallel.

Therefore, AB and CD are parallel.

For proving ABCD a trapezium,

Slope of AB = Slope of CD

Slope of AB = (-1 + 1)/(2 + 5) = 0

Slope of CD  = (1 - 1)/(-2 - 1) = 0

Hence, the quadrilateral is a trapezium.

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