Construct the perpendicular bisector segment FG.Construct a segment from the focus to the point on the directrix (segment FG).Construct two points, one as the focus (F) and one on the directrix (G).Construct a line (d) that will serve as the directrix.(Instructor Note: A Sketchpad file illustrating the simulation using the animate feature has been saved as parabola-animate.gsp.)Īll three constructions start in a similar manner. Specific steps have been recorded below for three different methods. There are several ways to simulate the activity in Part 1, using different features of The Geometer's Sketchpad. Carry out your construction using The Geometer's Sketchpad. Write down the key steps of the construction and share your ideas with the class. With your neighbor, plan a geometric construction we could use to simulate the folding process as described in Part 1.Instead, we are going to simulate the activity using The Geometer's Sketchpad. Part 2: Parabola as loci of lines To see the pattern described in Part 1 distinctly, we would have to fold the paper dozens of times. Make a conjecture about the relationship of the distance from the focus to the boundary, and the distance from the boundary to the directrix.Describe the boundary of the shape of the area containing the focus that is bounded by all of the fold lines. Flatten out your paper and look for any geometric patterns. We are interested in the pattern of the creases that are formed when point F is folded along the directrix. Continue this process approximately ten more times so that each time point F falls on a different location of the directrix. Again, deliberately crease your wax paper so that you can easily see the fold. Fold your wax paper so that point F falls anywhere along the directrix.Conjecture any relationships you might see between the line segment FG and the folded line. Fold your paper so that the two points are concurrent, and deliberately crease it so that you can easily see the fold mark when the paper has been flattened out. Using your straightedge, construct the line segment FG.Construct another point anywhere on the line, and label it G. Construct a point anywhere on the paper, except on the line, and label it F. ![]() With a straight edge, construct a line on your piece of wax paper.
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