We have two transverse wave
$$y_1= A\sin(kx-\omega t)$$
These two waves superposed. Then, at point $x=0$ the equation would be
$$y_1 + y_2 =-2A\sin\omega t.$$
Now how can we know at $x=0$ is node, antinode or neither of them .
In my book it is given as antinode .