let us illustrate each reflection with a picture:
x -axis reflection (reflecting across the x -axis)
y - axis reflection (reflecting across the y-axis)
From the pictures, we can see that in reflections across the x-axis, the original and reflected point are on a vertical line. This means that they have the same x-coordinate. This means that reflections across the x-axis keep the x-coordinate intact and they multiply the y-coordinate by -1 (so, for example, the reflection of the point (1,2) across the x-axis is (1,-2)).
In the same manner, we see that in reflections across the y-axis, the original and reflected point are on a horizontal line. This means that they have the same y-coordinate. This means that reflections across the y-axis keep the y-coordinate intact and they multiply the x-coordinate by -1 (so, for example, the reflection of the point (1,2) across the y-axis is (-1,2)).
