When a polygon reflects across the y axis ,how do the coordinates of the points change

The y coordinate will stay the same. The x coordinate will flip from positive to negative, or vice versa.

Some examples:
(1,2) > (-1,2)
(-3,4) > (3,4)
(-1.2, 8) > (1.2, 8)

The general rule is 
(x,y) > (-x, y)
indicating that only the x coordinate undergoes a change