Elliptic curve point addition clarification In a book I am reading currently, it asks to perform the addition of $(2,7)$ and $(5,2)$ in the elliptic curve defined as $y^2=x^3+2x+2 \mod 17$.

Now, I believe this is impossible, as these points are not part of the group, hence it is not possible to compute the third point. Is that correct?

Pretty sure I am correct, but just would like clarification that i'm not making a huge mistake, as this book has not had any errors so far so I'm suprised to see one.
What happens if you naively plug those numbers into the addition formula?  Anything obviously untoward?

This may be an exercise in the impact of invalid-curve attacks.