Keep the y-coordinate of the point the same. Remember that the opposite of a number is the number itself with its sign changed.
Reflection in they-axis
( x, y) → (- x, y)
Let's consider some examples. First, we will reflect a point where the x-coordinate is negative.
(- 2,1)
The first coordinate becomes its opposite. The opposite of - 2 is 2. The second coordinate stays the same.
Reflection in they-axis
( - 2, 1) → (2, 1)
Notice that the x-coordinate of the new point is positive. Let's look at another example, this time where the x-coordinate starts out positive.
(3, - 5)
Once again, we keep the second coordinate the same and the first coordinate becomes its opposite. The opposite of 3 is - 3.
Reflection in they-axis
( 3, - 5) → (- 3, - 5)
In this case the new point has a negative x-coordinate. We found both an example and a counterexample to the statement.
When a point is reflected across the y-axis, the new point has a negative x-coordinate.
