Montezumas Treasure

1
Montezumas Treasure
Montezuma, Aztec emperor (1480-1520), buried a
treasure in Tenochtitlan (Tanochtetlän - Present
day Mexico City) over 500 years ago.
Archeologists recently discovered a map showing
the location of the treasure. The location has
generated quite a bit of media attention, much to
the dismay of the archeologists.
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In order to allow both the media and
archeologists to work together, officials have
decided to build a rectangular fence around the
archeological dig, allowing the media access to
the site, yet allowing the archeologists room to
work.

• The points A, B, and C that you will be given
  will be the triangular area of the archeological
  dig. Your group will be responsible for
  constructing the fence around the site to protect
  the archeologists.

3
Points

• Problem 1 A(3, 12) B(-8, 4) C(2, -8)
• Problem 2 A(-5,-10) B(7, 4) C(-1, 9)
• Problem 3 A (-6,-7) B(7, -4) C(2, 5)
• Problem 4 A (8, -6) B(3, 8) C(-9, -3)
• Problem 5 A(-4,11) B(7, 8) C(-2, 6)
• Problem 6 A(6, 10) B(-3, 2) C(4, -9)
• Problem 7 A(9, 12) B(-1, 6) C(6, -5)
• Problem 8 A(-4,10) B(10, 6) C(2, -7)
• Problem 9 A (-8,9) B (4,5) C(-3, -12)
• Problem 10 A (8,9) B (3,-12) C(-6,5)

4
YOUR TASKS

• The person with the Green paper works the green
  questions
• The person with the red paper works the red
  questions
• The person with the blue paper works the blue
  questions.
• YOU WILL NEED TO HELP EACH OTHER!!!
• On day 3 I will give you presentation paper!

5
Student Activities

• Graph, label and connect points A, B and C which
  are the corners of the archeological dig site.
• Find the domain of triangle ABC
• Find the range of triangle ABC
• Create the smallest rectangle possible to create
  the boundaries for the media. This should
  enclose the triangle and use point A as a vertex
  of the both the triangle and rectangle.
• Label the rectangle ADEF so that point B is
  between point D and E and point C is between E
  and F.

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Student Activities Cont.

• Calculate length of side AB
• Calculate length of side BC
• Calculate length of side AC
• Find the perimeter of the archeological site,
  triangle ABC
• Find the total length of fencing needed to
  enclose rectangle ADEF

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• Find the area enclosed by the fence
• Find the area of right triangle ADB
• Find the area of right triangle BEC
• Find the area of right triangle CFA
• Find the area of the archeological dig site

8

• Write the equation in point-slope form of side AB
• Write the equation in point-slope form of side BC
  
• Write the equation in point-slope form of side AC
  
• Graph all three equations using your calculator
  show the teacher once you are complete.

9

• Archeologists have narrowed their search
• for the treasure by finding the midpoint of
• each side of the triangle.

10

• Calculate the coordinates for the midpoint of
  side AB label this point X
• Calculate the coordinates for the midpoint of
  side BC label this point Y
• Calculate the coordinates for the midpoint of
  side AC label this point Z
• Connect points X, Y and Z to create a
• triangle.

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BONUS

• The sides of triangle XYZ are half as long as
  those of triangle ABC. Is the area of triangle
  XYZ half the area of triangle ABC? Explain your
  answer in complete sentences.
• Honors Using the calculator graph the
  equations on their specified domain.

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• Watch out for Montezumas Revenge!!!
• (He!He!He!)