NAME THE TYPE OF QUADRILATERAL FORMED BY CONNECTING THE POINTS

Name the Type of Quadrilateral Formed by Connecting the Points :

In this section, we will see some examples to examine which type of quadrilateral formed by connecting the given points.

Name the Type of Quadrilateral Formed by Connecting the Points

Example 1 :

Name the type of quadrilateral formed. If any, by the following points and give reasons for your answer:

(i) (-1, -2) (1, 0) (-1, 2) (-3, 0)

Solution :

Let the given points as A(-1, -2)  B(1, 0)  C(-1, 2) and D (-3, 0)

Distance between two points  =  √(x2 - x1)2 + (y2 - y1) ²

Length of the side AB :

Here, x1  =  -1, y1  =  -2, x2  =  1  and  y2  =  0

=  √(1-(-1))2 + (0-(-2))2

=  √(1+1)2 + 22

=  √4 + 4

=  √8

Length of the side BC :

Here, x1  =  1, y1  =  0, x2  =  -1  and  y2  =  2

=  √(-1-1)2 + (2-0)2

=  √(-2)2 + 22

=  √4 + 4

=  √8

Length of the side CD :

Here, x1  =  -1, y1  =  2, x2  =  -3  and  y2  =  0

=  √(-3-(-1))2 + (0-2)2

=  √(-3+1)² + (-2)²

=  √4 + 4

=  √8

Length of the side DA :

=  √(-1-(-3))2 + (-2-0)2

=  √(-1+3)2 + (-2)2

=  √4 + 4

=  √8

AB = BC = CD = DA. Since length of all sides are equal, the given points are the vertices of square.

(ii) (-3, 5) (3, 1) (0, 3) (-1, -4)

Solution :

Let the given points as A(-3,5)  B(3,1)  C(0,3) and D (-1,-4)

Distance between two points  =  √(x2 - x1)2 + (y2 - y1) ²

Length of the side AB :

Here, x1  =  -3, y1  =  5, x2  =  3  and  y2  =  1

=  √(3-(-3))2 + (1-5)2

=  √(3+3)2 + (-4)2

=  √36 + 16

=  √52

Length of the side BC :

Here, x1  =  3, y1  =  1, x2  =  0  and  y2  =  3

=  √(0-3)² + (3-1)²

=  √(-3)² + (2)²

=  √9 + 4

=  √13

Length of the side CD :

Here, x1  =  0, y1  =  3, x2  =  -1  and  y2  =  -4

=  √(-1-0)2 + (-4-3)2

=  √(-1)² + (-7)²

=  √1 + 49

=  √50

Length of the side DA :

Here, x1  =  -1, y1  =  -4, x2  =  -3  and  y2  =  5

=  √(-3-(-1))² + (5-(-4))²

=  √(-3+1)² + (5 +4)²

=  √4 + 81

=  √85

The length of all sides of quadrilateral are of different. Therefore, it can be observed that it is only a quadrilateral. After having gone through the stuff given above, we hope that the students would have understood, name the type of quadrilateral formed by connecting the points.

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