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Name the Type of Quadrilateral Formed, If Any, by the Following Point, and Give Reasons for Your Answer (4, 5), (7, 6), (4, 3), (1, 2) - CBSE Class 10 - Mathematics

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Question

Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer (4, 5), (7, 6), (4, 3), (1, 2)

Solution

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.

`:.AB = sqrt((4-7)^2+(5-6)^2) = sqrt((-3)^2+(-1)^2) = sqrt(9+1) = sqrt10`

`BC =sqrt((7-4)^2+(6-3)^2) = sqrt((3)^2+(3)^2) = sqrt(9+9) = sqrt18`

`CD = sqrt((4-1)^2+(3-2)^2) = sqrt((3)^2+(1)^2) = sqrt(9+1) = sqrt10`

`AD = sqrt((4-1)^2+(5-2)^2) = sqrt((3)^2+(3)^2) = sqrt(9+9) = sqrt18`

Diagonal AC =`sqrt((4-4)^2+(5-3)^2) = sqrt((0)^2+(2)^2) = sqrt(0+4) = 2`

Diagonal CD =`sqrt((7-1)^2 + (6-2)^2) = sqrt((6)^2+(4)^2) = sqrt(36+16) = sqrt52 = 13sqrt2`

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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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 7: Coordinate Geometry
Ex. 7.10 | Q: 6.3 | Page no. 161

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Solution Name the Type of Quadrilateral Formed, If Any, by the Following Point, and Give Reasons for Your Answer (4, 5), (7, 6), (4, 3), (1, 2) Concept: Distance Formula.
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