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  • Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)

6.(i) Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
     (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)

Answers (1)

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Let the given points (-1,-2),\ (1,0),\ (-1,2),\ and\ (-3,0) be representing the vertices A, B, C, and D of the given quadrilateral respectively.

The distance formula:

D = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}

AB= \sqrt{(-1-1)^2+(-2-0)^2} =\sqrt{4+4} = \sqrt{8} = 2\sqrt2

BC= \sqrt{(1+1)^2+(0-2)^2} =\sqrt{4+4} = \sqrt{8} = 2\sqrt2

CD= \sqrt{(-1+3)^2+(2-0)^2} =\sqrt{4+4} = \sqrt{8} = 2\sqrt2

AD= \sqrt{(-1+3)^2+(-2-0)^2} =\sqrt{4+4} = \sqrt{8} = 2\sqrt2

Finding the length of the diagonals:

AC= \sqrt{(-1+1)^2+(-2-2)^2} =\sqrt{0+16} = 4

BD= \sqrt{(1+3)^2+(0-0)^2} =\sqrt{16+0} = 4

It is clear that all sides are of the same lengths and also the diagonals have the same lengths.

Hence, the given quadrilateral is a square.

Posted by

Divya Prakash Singh

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