Q:

How do you graph a reflection across the x axis?

A:

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).

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Credit: Izabela Habur E+ Getty Images

1. 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.

2. 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.

3. 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.

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