Question

draw the quadrilateral formed by the points whose vertices are given below and name the type of quadrilateral
(1,-1),(-1,3),(1,7) and (3,3)

(using distant formual)​

Answer 1

Answer:

Distance formula

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

i)

A(−1,−2),B(1,0),C(−1,2),D(−3,0)

Vertices: AB=2

2

,BC=2

2

,CD=2

2

,AD=2

2

Diagonals: AC=4,BD=4

Since, all sides and both the diagonals are same.

ABCD is a square.

ii)

A(−3,5),B(3,1),C(0,3),D(−1,−4)

Vertices: AB=

52

,BC=

13

,CD=

50

,AD=

85

Diagonals: AC=

13

,BC=

13

Since, all sides are not equal to each other and both the diagonals are same.

ABCD is a quadrilateral.

iii)

A(4,5),B(7,6),C(4,3),D(1,2)

Vertices: AB=

10

,BC=

18

,CD=

10

,AD=

18

Since, opposite sides are equal.

ABCD is a parallelogram.