$\"\"$

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The vertices of quadrilateral ABCD are $\"\"$ .

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Let AB, BC, CD and DA are adjacent sides of the quadrilateral.

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The vertices of line AB are $\"\"$ .

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Substitute the values of $\"\"$ in the slope formula $\"\"$ .

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$\"\"$ .

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The slope of line AB is $\"\"$ . $\"\"$

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The vertices of line BC are $\"\"$ .

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Substitute the values of $\"\"$ in the slope formula $\"\"$ .

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$\"\"$ .

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The slope of line BC is $\"\"$ . $\"\"$

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The vertices of line CD are $\"\"$ .

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Substitute the values of $\"\"$ in the slope formula $\"\"$ .

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$\"\"$ .

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The slope of line CD is $\"\"$ . $\"\"$

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The vertices of line DA are $\"\"$ .

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Substitute the values of $\"\"$ in the slope formula $\"\"$ .

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$\"\"$ .

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The slope of line DA is $\"\"$ .

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The slopes of adjacent sides AB, BC, CD and DA of the quadrilateral are $\"\"$ respectively.

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The slopes of adjacent sides AB, BC, CD and DA of the quadrilateral are negative reciprocals, so the adjacent sides are perpendiculars. Therefore quadrilateral ABCD is rectangle. $\"\"$

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Yes, the quadrilateral ABCD is rectangle.