Because it has been decided that the right and upwards directions in a plane are the positive directions and the left and downwards are negative. Originally, the decisions were arbitrary but conventionally agreed (in the same sort of way that North is usually shown at the top of a map).
Any displacement in a positive direction is called a positive displacement.
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south
Indeed it is.
They are the locations where the amplitudes of the two waves combine destructively. The positive displacement of one wave is exactly matched by the negative displacement of the other so that the overall displacement is zero.
It is called the displacement in the horizontal direction.
displacement