Math, asked by amruthagowda7411, 5 months ago

if (-2,-1)A, C=4b, B =1,2 are the vertices of parallelogram. Find the value of AB

Answers

Answered by hardworkingstudent1
0

Answer:

xb

Step-by-step explanation:

Given sides of parallelogram A(−2,1),B(a,0),C(4,b),D(1,2)

We know that diagonals of Parallelogram bisect each other.

Mid-point let say O of diagonal AC is given by

x=(

2

x

1

+x

2

)and y=(

2

y

1

+y

2

)

O (

2

−2+4

,

2

1+b

) ..................(1)

Mid-point let say P of diagonal BD is given by

P (

2

a+1

,

2

0+2

) ..................(2)

Points O and P are same

Equating the corresponding co-ordinates of both midpoints, we get

2

−2+4

=

2

a+1

⇒a=1

and

2

1+b

=

2

0+2

⇒b=1

Now the Given co-ordinates of the parallelogram are written as

A(−2,1),B(1,0),C(4,1),D(1,2)

By distance formula,

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

we can find the length of each side

AB=

(−2−1)

2

+(1−0)

2

AB=

(3)

2

+(1)

2

=

10

AB=CD ...............(pair of opposite sides of the parallelogram are parallel and equal)

BC=

(4−1)

2

+(1−0)

2

BC=

(3)

2

+(1)

2

=

10

BC=AD ...............(pair of opposite sides of the parallelogram are parallel and equal )

⇒AB=BC=CD=AD=

10

⇒ABCD is a Rhombus

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