How Do You Graph a Reflection Across the X Axis?
To reflect an image across the x-axis, the image's y coordinates must be flipped. This means that if an image has the x and y coordinates (x, y) of (3, 2), (4, 4) and (5, 2), the reflected image must have the coordinates (3, -2), (4, -4) and (5, -2).
- Determine the coordinates of the original image
Determine the original image's coordinates, and write them down in (x, y) format. The x axis is always the horizontal line on a graph, while the y axis is always the vertical line on a graph. Draw a line from coordinate to coordinate to ensure that the reflected image matches the original image.
- Flip the y coordinates of the original image
Determine how the y coordinates should be flipped. Positive y coordinates must become negative – that is, (x,y) changes to (x,-y) – while negative y coordinates must become positive – (x,-y) changes to (x, y). Write down the reflected image's coordinates next to the original image's list of coordinates.
- Plot the coordinates of the reflected image
Use the new list of coordinates to plot the reflected image on the graph. Draw a line from coordinate to coordinate to provide visual proof that the new image properly reflects the original image.