Investigating Line Segments
Hold down the shift key and click and drag on the window to move the axes. Hold down the shift key and scroll down/up to zoom in/out. In this application, you can move the points A, B, and C by clicking and dragging them. You can also turn the displayed distances on or off, or turn point B on or off.
 Place A, B, and C so that B is between A and C. What do you notice about the distances?  Place A, B and C so B is the midpoint of segment AC. How do you know that B is the actual midpoint?  Place A, B and C so B is between A and C and AB=BC. What do you notice about the figure?  Can you have AB=BC but not have B between A and B? If so, give the points. If not, why not? Uncheck “Show Distances”.  Use the points to create a right triangle where segment AC is the hypotenuse. Calculate the distance AC by hand. Then check your answer by clicking “Show Distances”. Were you correct? Do you notice any patterns that include the distances AB and BC? Check “Show Distances” and uncheck “Show Point B”.  Can you find any points for A and C where AC is a whole number? Describe your results and explain them.  Play around with the program. Look for patterns. If you think you see something that might be true, make a conjecture.