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Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

(i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)

(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)

(iii) (4, 5), (7, 6), (4, 3), (1, 2)

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(i) Let the points (−1, −2), (1, 0), (−1, 2), and (−3, 0) be representing the vertices A, B, C, and D of the given quadrilateral respectively. Diagonal AC Diagonal BD It can be observed that all sides of this quadrilateral are of the same length and also, the diagonals are...
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(i) Let the points (−1, −2), (1, 0), (−1, 2), and (−3, 0) be representing the vertices A, B, C, and D of the given quadrilateral respectively.

Diagonal AC

Diagonal BD

It can be observed that all sides of this quadrilateral are of the same length and also, the diagonals are of the same length. Therefore, the given points are the vertices of a square.

(ii)Let the points (− 3, 5), (3, 1), (0, 3), and (−1, −4) be representing the vertices A, B, C, and D of the given quadrilateral respectively.

It can be observed that all sides of this quadrilateral are of different lengths. Therefore, it can be said that it is only a general quadrilateral, and not specific such as square, rectangle, etc.

(iii)Let the points (4, 5), (7, 6), (4, 3), and (1, 2) be representing the vertices A, B, C, and D of the given quadrilateral respectively.

Diagonal AC

Diagonal BD

It can be observed that opposite sides of this quadrilateral are of the same length. However, the diagonals are of different lengths. Therefore, the given points are the vertices of a parallelogram.

 
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the points of option i , forms a square of side √8 units on the Cartesian plane.
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Professor with Masters degree (USA)

(i) It forms a square
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Tutor

Option 1 by using distance formula we get all four sides are equal so it can be a square And the third by using the same formula we get opposite sides are equal it can be a rectangle
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ð???ð??¯ results which will improve your position.

(1) (-1, -2),(1,0), (-1,2),(-3,0) let the point be A(-1,-2), B(1,0) C(-1,2) D(-3,0)
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