The following applet allows you to explore with a triangle reflection over the x-axis. Your goal is to take the blue triangle and drag A'', B'', and C'' so that it matches the reflection of the pre-image of triangle with vertices A, B, and C. When you think you have the correct reflection of the image, check "Check Answer" and you will be able to see if you have correctly moved the vertices.
Jot down the coordinates of A, B, and C. When you are able to correctly match up the reflection of this image, jot down the correct coordinates for A'', B'', and C''. What do you notice? Continue to jot down the coordinates of the pre-image and image and see if you can make a conjecture.