please help me with the question and explain in detail ( second part only)thanks
ID: 2944220 • Letter: P
Question
please help me with the question and explain in detail ( second part only)thanks
in one of your worst nightmares you are a contestant on a TV game show that is
designed to make you look silly. You and two other contestants have been placed at
the mid-points of the edges of a triangle (one contestant per edge). Each contestant
has a pet flea that is sitting on the opposing vertex. These are specially trained
homing fleas, once released from their vertex prisons they will travel in a straight
line to their loving owners (i.e., you). The winner is the person who is rst re-united
with their pet flea. Your triangle has sides of length 6, 9 and 11 metres and your
pet fleas are in top shape having been recently measured (with a flea-radar gun)
to run at a staggering 0.666 m/sec. You are on the side of length 9 metres.
All 3fleas are released at the same time. Are you a winner? (A simple yes/no answer
will not suce, you should explain how you came to your answer.)
Second part
Then if fleas have been equipped with special little boots that leave a distinct trail
as they run home (to you). Thus each flea draws a line over the triangle. What
interesting fact can you deduce about the three lines drawn by the fleas?
You can assume here that to the human eye the lines are continuous
(in reality they aredotted lines, one dot for each boot print, but the dots are so
small and so close we don't notice the individual dots seeing instead a steady straight line).
in the second part of this question you are not required to prove your claims,
you can just state the result. But if you do so then you should provide a reference
(book,web page etc.) so that we can see where you got your result from. But
beware of the internet { it is a great resource but some web pages con-
tain incorrect information. You should look up a few sources to see that
they all agree.
Explanation / Answer
The dotted lines bisect the angles of their respective verteces. They also intersect at a point known as the centroid (you have to look this up if you don't know what it is). The centroid is found 2/3 of each respective distance. Lets say one of the fleas has to travel 6 meters and another 9m. That means it will be at the centroid at 4m from its starting vertex for the first one, and 6m for the second. That also means that after the centroid, only 1/3 of the distance remains. For the first flea, that means it has to travel 2m more; while, the second flea has 3m more.
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