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Name the type of quadrilateral formed, if any, by the given points, and give reasons for your answer: (- 1, - 2), (1, 0), (- 1, 2), (- 3, 0) - CBSE Class 10 - Mathematics

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Question

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

Solution

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.

`:.AB = sqrt((-1-1)^2+(-2-0)^2) = sqrt((-2)^2+(-2)^2) = sqrt(4+4) = sqrt8 = 2sqrt2`

`BC = sqrt((1-(-1))^2+(0-2)^2) = sqrt((2)^2+(-2)^2) = sqrt(4+4) = sqrt8 =2sqrt2`

`CB = sqrt((-1-(-3))^2+(2-0)^2) = sqrt((2)^2+(2)^2) = sqrt(4+4) = sqrt8 = 2sqrt2`

`AD = sqrt((-1-(3))^2 + (-2-0)^2) = sqrt((2)^2+(-2)^2) = sqrt(4+4) = sqrt8 =  2sqrt2`

Diagonal AC =`sqrt((-1-(-1))^2+(-2-2)^2) = sqrt(0^2+(-4)^2) = sqrt(16) = 4`

Diagonal BD =`sqrt((1-(-3))^2+(0-0)^2) = sqrt((4)^2+0^2) = sqrt16 = 4`

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.

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 7: Coordinate Geometry
Ex. 7.10 | Q: 6.1 | Page no. 161

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Solution Name the type of quadrilateral formed, if any, by the given points, and give reasons for your answer: (- 1, - 2), (1, 0), (- 1, 2), (- 3, 0) Concept: Distance Formula.
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