Sketchpad - Reservoir Between Three Villages
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.
Is the equidistant point always the best point to use for the