Question

show that the point a(4,3),b(1,2),c(1, 0),d(4,1)r vertices of a parallelogram and find the length of its digonals​

Answer 1

ANSWER
For a rectangle, the opposite sides need to be equal and diagonals also have to be equal.

Now by using

Distance Formula =
(x
2
​
−x
1
​
)
2
+(y
2
​
−y
1
​
)
2

​


Here coordinates of A are x
1
​
and y
1
​

and coordinates of B are x
2
​
and y
2
​

Similarly for other coordinates also.
Length AB=
(−2+4)
2
+(−4+1)
2

​


=
13
​


Length BC=
(4+2)
2
+(0+4)
2

​


=
52
​


Length CD=
(2−4)
2
+(3−0)
2

​


=
13
​


Length DA=
(−4−2)
2
+(−1+3)
2

​


=
52
​


Diagonal AC=
(4+4)
2
+(0+1)
2

​


=
65
​


Diagonal BD=
(2+2)
2
+(3+4)
2

​


=
65
​

ABCD are the vertices of a rectangle since AB=DC and AD=BC, also diagonal AC=BD.

Answer 2

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