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HW # 5
Other Trees
The idea of this
assignment is to bring out the idea about
symmetry.
Visit the above link and learn as much as you can
about symmetry. You will be using that knowledge in the next activities.
Homework #5 Page. 77
Question 1
1. Begin this homework by graphing the center
(0,0) of the orchard in the center of a graph paper.
2. Draw the tree located at (5, 12). This
tree is on the boundary of the orchard.
2a. Find the radius of that orchard using
the distance formula. Explain the result of this calculation and indicate that
"every tree located at the same distance (radius) than the (5, 12) tree will
also be on the boundary (or border) of the Orchard.
3. Use the symmetry concept to locate the
coordinates of the other trees that must be also on the boundary.
You should localize 12 points on the boundary.
Make sure to discuss your findings with your group.
Did you use the symmetry concept to find the 12
points?
Explain.
Did you use the Pythagorean Theorem to find the
radius? Explain.
How are the distance between the points (0, 0)
and the radius of the orchard related? Explain
What can you say about the coordinate (0, 13)
Where the 13 came from? Explain.
How would you explain that if the point (-a, -b)
is on the circle, then so is (a, b)?
Compare (-5)2
with (5)2.
What do you notice? Can you explain,
mathematically, why ?
Question 2
Now you are ready to generalize.
2a. Do exactly what you did with the coordinate
(5, 12) but using the general location (a, b)
and find the radio r of that orchard.
What other trees must also be on the boundary of
the new orchard?
Remember: Make your answer as complete as
possible.
If you can't see any "important details
follow the hint given by your textbook. (p. 77)
Analyze your result and if you can pick a
different length for the radius. Graph your results and plain what you see.
You can practice graphing it
here
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Mr. Lora |
