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In a recatngle ABCD, the coordinates of ...

In a recatngle ABCD, the coordinates of A and B are (1, 2) and (3, 6) respectively and some diameter of the circumscribiling circle of ABCD has equation `2x-y+4=0`. Then the area of the rectangle is -

A

16

B

`2sqrt(10)`

C

`2sqrt(5)`

D

20

Text Solution

Verified by Experts

The correct Answer is:
A

Slope of `AB=4/2=2`
Slope of `BC=-1/2`
`l(AB)=sqrt(4+16)=2sqrt(5)`
distance between `2x-y+4=0` & `2x-y=0 rArr 4/sqrt(5)`
Area `=2sqrt(5). 8/sqrt(5)=16`
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