5)Find the distance between the following pairs of points `A(a,0), B(0,a)`

Explanation

`A(a,0)` and `B(0,a)`
Let `A(x_(1),y_(1))` and `B(x_(2),y_(2))`
then `x_(1)=a,y_(1)=0,x_(2)=0` and `y_(2)=a`
By distance formula
`d(A,B)=sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2))`
`=sqrt((0-a)^(2)+(a-0)^(2))`
`=sqrt((-a)^(2)+a^(2))`
`=sqrt(a^(2)+a^(2))`
`=sqrt(2a^(2))`
`=sqrt(2a)`
`d(A,B)=sqrt(2a)`