The points A ( - 1, - 2), B (4, 3), C (2, 5) and D ( - 3, 0) are in that order form a rectangle.


True

We know that, in a rectangle, opposite sides and diagonals are equal and bisect each other



Calculate the distance between A ( - 1, - 2) and B (4, 3);


By using the distance formula;


Distance between the points (x1, y1) and (x2, y2);



So,





Distance between C (2, 5) and D ( - 3, 0);





Distance between A ( - 1, - 2) and D ( - 3, 0);


AD =




Distance between B (4, 3) and C (2, 5);


BC =




Since, AB = CD and AD = BC


Also, Calculate the distance of diagonals;


Distance between A ( - 1, - 2) and C (2, 5);


AC =




Distance between D ( - 3, 0) and B (4, 3);


DB =




Since, diagonals AC and BD are equal


Hence, the points A ( - 1, - 2), B (4, 3), C (2, 5) and D ( - 3, 0) form a rectangle.


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