Doug C. answered • 02/19/25
Math Tutor with Reputation to make difficult concepts understandable
When you reflect a point over the y-axis the y-coordinate of the image does not change. The line segment joining the original points and its reflection is perpendicular to the y-axis. The point where that line segment intersects the y-axis is the midpoint of that segment. That point of intersection in this case would be (0,1). The distance from (-3, 1) to (0,1) is 3. So the reflection is the same distance on the other side of the y-axis. or (3,1).
This graph shows the line segment joining (-3,1) and (3,1) along with its midpoint. It also shows draggable points P and Q that are reflections of each other over the y-axis. The shortcut for reflecting a general point (x, y) over the y-axis is simply (-x, y), i.e. take the opposite of the x-coordinate and leave the y-coordinate the same.
desmos.com/calculator/xm7sclggbg
