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Let A=(a(1),a(2)) " and " B=(b(1),b(2)) ...

Let `A=(a_(1),a_(2)) " and " B=(b_(1),b_(2))` be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between A an B ?

A

`sqrt(65)`

B

`sqrt(74)`

C

`sqrt(83)`

D

`sqrt(97)`

Text Solution

Verified by Experts

The correct Answer is:
C
`AB=sqrt((a_(1)-b_(2))^(2)+(a_(2)-b_(2))^(2))`
Squrare + Square = `sqrt(65)` possible when
`=64+1`
`sqrt(74)=49+25`
`sqrt(97)= 81+16`
But `sqrt(83)` not possible.
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