Math, asked by shilpapatel0166, 5 hours ago

13. Name the quadrilateral formed, if any, by the
following points and give reasons for your answer.
(i) A(-1, -2), B(1, 0), C(-1, 2), D(-3, 0)
(ii) A(-3, 5), B(3, 1), C(O, 3), D(-1, -4)​

Answers

Answered by seemanjadhav83
0

Answer:

(i) Let the given points are A(−1,−2), B(1,0), C(−1,2)and D(−3,0) Then,

AB=

(1+1)

2

+(0+2)

2

=

2

2

+2

2

=

4+4

=

8

BC=

(−1−1)

2

+(2−0)

2

=

(2

2

+2

2

)

=

4+4

=

8

CD=

((−3)−(−1))

2

+(0−2)

2

=

2

2

+(−2)

2

=

4+4

=

8

DA=

(−3)−(−1))

2

+(0−(−2))

2

=

(−2)

2

+2

2

=

4+4

=

8

AC

((−1)−(−1))

2

+(2−(−2))

2

=

0+4

2

=

16

=4

BD=

(−3−1)

2

+(0−0)

2

=

−4

2

=

16

=4

Since the four sides AB,BC,CD and DA are equal and the diagonals AC and BD are equal .

∴ Quadrilateral ABCD is a square.

(ii)Let the given points are A(−3,5),B(3,1),C(0,3) and D(−1,−4)Then

AB=

(−3−3)

2

+(5−1)

2

=

(−6)

2

+4

2

=

36+16

=

52

BC=

(3−0)

2

+(1−3)

2

=

(3

2

+(−2)2

2

)

=

9+4

=

11

CD=

(0−(−1))

2

+(3−(−4))

2

=

1

2

+(7)

2

=

1+49

=

50

DA=

(−1)−(−3))

2

+((−4)−5))

2

=

(2)

2

+(−9)

2

=

4+81

=

85

Here AB

=BC

=CD

=DA

∴ it is a quadrilateral.

(iii)Let the given points are A(4,5),B(7,6),C(4,3) and D(1,2)Then

AB=

(7−4)

2

+(6−5)

2

=

3

2

+1

2

=

9+1

=

10

BC=

(4−7)

2

+(3−6)

2

=

((−3)

2

+(−3)

2

)

=

9+9

=

18

CD=

(1−4)

2

+(2−3)

2

=

(−3)

2

+(−1)

2

=

9+1

=

10

DA=

(1−4)

2

+(2−5)

2

=

(−3)

2

+(−3)

2

=

9+9

=

18

AC

(4−4)

2

+(3−5)

2

=

0+(−2)

2

=

4

=2

BD=

(1−7)

2

+(2−6)

2

=

(−6)

2

+(−4)

2

=

36+16

=

52

Here AB=CD,BC=DA . But AC

=BD

Hence the pairs of opposite sides are equal but diagonal are not equal so it is a parallelogram.

Answered by Silentheart0
1

Step-by-step explanation:

(i). Here, AB = BC = CD = AD and AC = BD

Since , all sides are equal and diagonals are equal, so given quadrilateral is a square.

(ii). Here, AC ≠ BC ≠ CD ≠ DA

Since, sides are not equal, thus only a general and not a specific quadrilateral

such as square or parallelogram is formed.

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