Shortest Path with Geometry Sketchpad

When on his annual camping trip along the St. Joe River, Jesse, took a hike up Marble Creek. Rounding the last bend in the trail on his return to the campsite, he could see up ahead that his tent was on fire. Jesse has camelback that holds a lot of water, but its empty. Jesse must run to the river fill his bucket and run to the burning tent to put out the fire. What’s the shortest path he can take?

• Construct a picture with a line segment AB representing the river.
• Anywhere along one side of the river place any point labeled J, representing where Jesse is standing.
• Anywhere along the same side of the river, as Jesse, place any point labeled T, representing the burning tent.
• Think about the path Jesse will run. He must first run to the river then to the burning tent.
• Mark the point along the river that you think would make the shortest distance for Jesse to run.
• Label this point R.
  

What is the shortest path possible?

Q1. What measurements could we make to be more accurate? Make the measurements of the lengths. Using the calculator cut and paste the measurements and add them together. You should see the length of the shortest path in your list of measurements on the screen. Then move the point until you think the distance is shortest.

Now, measure the angles <JRA and <TRB. Move things around and observer what happens to the two angles.

Q2 Make a conjecture about the angles when the path is shortest. Write your conjecture.
Q3. Move Jesse and observe what happens. Move the burning tent and observe what happens. Move the river and observe what happens. Make a conjecture on their relationship based on the data and your observations.