# 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) - Mathematics

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 Class 10 Maths
Chapter 7 Coordinate Geometry
Exercise 7.1 | Q 6.3 | Page 161