Sketchpad - Reservoir Between Three Villages

Tools

Arrowhead      
Point              
Compass          
Straight Edge      
Alphabet      
Script View      


Sketchpad Exploration

  • Choose the Point Tool and create three points that represent the three villages.
  • Use the Point Tool to create a fourth point that represents your guess as to where the reservoir should be.
  • Choose the Arrowhead Tool and click on the white background to ensure that nothing is chosen.
  • Hold down the shift key and choose the points representing village one and the reservoir. Notice that they will both be selected.
  • Under Measure release on Distance
  • Repeat to measure the distance between village two and the reservoir, and village three and the reservoir. Be sure that you click on the white background each time to ensure that nothing else is chosen.
  • Choose the point representing your reservoir and drag it until the distance to each village is approximately the same.

  • Choose the Straight Edge Tool and connect the three villages with segments by clicking down on one point, releasing, moving to the other point, and clicking down again. Notice that the point will become a bright red when you move your mouse over it.
  • Choose the Arrowhead Tool and choose one side of the triangle that you have formed. Under Construct release on Midpoint.
  • Use the Arrowhead Tool to choose the midpoint and the line it is on. Under Construct release on Perpendicular Line
  • Repeat to construct the perpendicular bisectors of the other 2 sides of your triangle. Be sure to click on the white background before you start to ensure nothing else is chosen.
  • Drag your reservoir guess on top of the intersection of the perpendicular bisectors (called the circumcircle) if it is not already there.
  • Now move the villages around so that they form different kinds of triangles (acute, obtuse, right). Drag the reservoir guess on top of the intersection of the perpendicular bisectors to verify that this intersection is always equidistant from the three villages.

    Follow-up Question Is the equidistant point always the best point to use for the reservoir? Why?