Need simple explanation on "Differentiation from first principles"

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I'm following this eBook, but couldn't understand how the author explains the points as $A(x,y)$ and $B(x+δx,y+δy)$. Why B has more arguments which are $+δx$ and $+δy$ than A?

Also, the height of B which is $f(x+\delta x)$, why it use the $+δx$ other than the height of A which is only $f(x)$?

part of the eBook