We plot the point (2,3):



Pretend that the point is a baseball and the y-axis is a mirror, and
you look into the mirror, where will you see the reflection of the
baseball?  It will be on the left of the y-axis, the same distance
from the y-axis:

 

So the image of (2,3) after a reflection over the y-axis is (-2,3).

Three kinds of reflections are over the y-axis, x-axis, and the origin.

In general, the image after a reflection of a point over the y-axis is
the point with the sign of the x-coordinate changed, but the y coordinate
remains the same.

In general, the image after a reflection of a point over the x-axis is
the point with the sign of the y-coordinate changed, but the x coordinate
remains the same.

In general, the image after a reflection of a point over the origin is
the point with the signs of BOTH coordinates changed.

Edwin