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  • Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (–3, 5), (3, 1), (0, 3), (–1, – 4)

6.(ii)   Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

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

Answers (1)

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Let the given points (-3,5),\ (3,1),\ (0,3),\ and\ (-1,-4) 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{(-3-3)^2+(5-1)^2} =\sqrt{36+16} = \sqrt{52} = 2\sqrt{13}

BC= \sqrt{(3-0)^2+(1-3)^2} =\sqrt{9+4} = \sqrt{13}

CD= \sqrt{(0+1)^2+(3+4)^2} =\sqrt{1+49} = \sqrt{50} = 5\sqrt2

AD= \sqrt{(-3+1)^2+(5+4)^2} =\sqrt{4+81} = \sqrt{85}

All the sides of the given quadrilateral have different lengths.

Therefore, it is only a general quadrilateral and not a specific one like square, rectangle, etc.

Posted by

Divya Prakash Singh

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