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Weekly Challenge 1/24




(p.s.) i was a little nervous making this video, as it was one of my first, so please excuse my stuttering and pausing)







As it isn't possible to make an applet for geogebra 3D yet, I took this picture. It demonstrates the properties of two 3D points, A and B, when added or subtracted.
3d_capture.PNGhttp://madeiramath2.wikispaces.com/John+M


This is my new and improved sigma translation applet. I've added a few sliders for additional reflections/rotations.


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This is another demonstration of the sequence function on Geogebra. As this applet has many sequences in it, i will not refer directly to the formulas like I did in my previous applet.

Try messing with the sliders, then mess with the vector. please enjoy.


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This applet demonstrates the ability of the sequence function in Geogebra, specifically the sequence:


-- Sequence[Circle[A a + 0.1 B' b, 4], b, -10, 10]


Please enjoy.

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GEOGEBRA ASSIGNMENT Due FRIDAY 11/5! Create and embed an applet on your wiki page that shows how the Altitudes, Perpendicular Bisectors, and Medians work. You should include a check box to hide and reveal things, as well appropriate 'DECORATIONS" to illustrate the correct markings on your triangle.You should also include some text to describe any significant features of the special segments.


Note: since this is an equilateral triangle, all the points (orthocenter, circumcenter, and centroid) are on the same coordinate point.


To see them individually, drag one or more points on the triangle.


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Problem #10 pg 16:

Positions of three points are described by the following three pairs of equations: { How do the positions of these objects compare at any given moment?

external image latex2png.2.php?z=100&eq=x%3D2-2texternal image latex2png.2.php?z=100&eq=%20y%3D5%2B7t

external image latex2png.2.php?z=100&eq=x%20%3D%204-2t%20external image latex2png.2.php?z=100&eq=y%20%3D%20-2%2B7t

external image latex2png.2.php?z=100&eq=x%3D2-2%28t%2B1%29external image latex2png.2.php?z=100&eq=y%20%3D%205%2B7%28t%2B1%29

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GEOGEBRA ASSIGNMENT: ( Found on the home page)


Create and embed an applet on your wiki page that show two points moving along paths that intersect at right angles. The paths should not be horizontal or


vertical. The points should be controlled by one slider. One point should move twice as fast as the other. The points should arrive at the intersection point 1 time unit


apart. You should trace your points so their paths can be easily seen. There are a number of examples of applets like these on solution pages.


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-Sky Diving Problem



check out this weird use of reflections



Paper folding problem:



(adjustments to the actual problem have been made to fit this applet)


For the paper folding picture below,

BD = 15 and AB = 20


a) if CG = 12, find GD, DF, BF. A thinking problem is to find the distance from G to A'. A challenging problem is to find the length of the fold.


b) Repeat when CG = 15


c) Repeat when CG = 7


d) let CG = x. Write an expression for the area of triangle GFD. Where should F be located to produce the greatest possible area?


e) Find the area of trapezoid EGFA'

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a) external image latex2png.2.php?z=100&eq=20-12%3DGD%3D8
external image latex2png.2.php?z=100&eq=%5Csqrt%7B12%5E2%20-8%5E2%20%7D%3DDF%3D%5Csqrt%7B80%7D
external image latex2png.2.php?z=100&eq=15-%5Csqrt%7B80%7D%3DBF%3D6.05573

b) external image latex2png.2.php?z=100&eq=20-15%3DGD%3D5
external image latex2png.2.php?z=100&eq=%5Csqrt%7B15%5E2%20-%205%5E2%7D%3DDF%3D%5Csqrt%7B200%7D
external image latex2png.2.php?z=100&eq=15-%5Csqrt%7B200%7D%3DBF%3D0.86

c) not possible because for CG =7, GD =8 and therefore the hypotenuse would have to be shorter// than one of the sides, which is impossible.

d) Area of external image latex2png.2.php?z=100&eq=%5CDelta%20GDF%3D%20%5Csqrt%7Bx%5E2%20-%20%2820-x%29%5E2%7D*%20%2820-x%29%2F2
to get the placement of F to get the maximum area, look at this graph:
external image latex2png.2.php?z=100&eq=Y%3D%20%5Csqrt%7Bx%5E2%20-%20%2820-x%29%5E2%7D*%20%2820-x%29%2F2
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When F is 13.28 from D, the Area ofexternal image latex2png.2.php?z=100&eq=%5CDelta%20GDF%3D38.49

e) divide the trapezoid into 3 identical right triangles, each having a short leg of 6 and a long leg of 15,
external image latex2png.2.php?z=100&eq=%286%20*%2015%29%20*%203%2F2%20%3D%20Area%20%3D%20135
Finished

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