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Buried Treasure

  • Classroom Resources / Problems of the Week

    Buried Treasure


    PoW ID: 3352

    Problem Print

    Callie was vacationing in the Caribbean when she found a treasure map made by the famous pirate Algebeard many years before:

    stump (1,11) rock (5,3) waterfall (26,2)


    On the back of the map was written:

    Start halfway between the rock and the old stump. Walk so that the distance between ye and the stump is always the same as the distance between ye and the rock. When ye be exactly northwest of the waterfall, ye be standing on my buried treasure.

    Using her algebra skills, Callie was able to determine exactly where Algebeard's loot was stashed. What are the coordinates where Callie should dig?

    Extra

    Extra: A lot of years have passed since Algebeard drew his map, and there are more stumps in the area now. Find a location for a tree stump that would make Algebeard's treasure impossible to find if it was used in the directions instead of the stump at (1,11). Explain why your location would make the directions not work.

    Answer Check

    Show Answer

    Callie should dig at (15,13) to find the treasure.

    Extra: Stump locations that would make the map impossible are (6,4), (7,5), (8,6), and so on. Any location such that the slope between the location and the rock is 1 will make the map useless.


    If your answer doesn't match ours,

    • did you realize that the line you need to walk is the perpendicular bisector of the segment joining the rock and the old stump ?
    • did you think about the slope of the line from the waterfall to the buried treasure?
    • did you find the equations of the two lines that intersect at the buried treasure?
    • did you find the common solution for those two linear equations?
    • did you check your math?

     If your answer does match ours,

    • is your explanation clear and complete? Will someone reading it fully understand how you came up with your answers?
    • did you make any mistakes along the way? If so, how did you find and fix them?
    • are there any hints that you would give another student?
    • did you have an "Aha!" moment? If so, describe it.
    • did you try the Extra?