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 (x_{1}, y_{1}) and (x_{2}, y_{2});

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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