Question

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)`

Answer 1

Correct Answer - 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.