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Triangle

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    Given the three points A (3,4,0) , B (8,0,6) , C (0,5,12) in space . find
    1)Area of the triangle ABC
    2)the length of the three medians of this triangle
    3)The measure of the angle ABC
    4)Equation of the plane ABC
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    what have you done so far?
  3. Offline

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    At least try it before coming on tsr with your homework questions... Why should we do it for you?
  4. Offline

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    "Sigh" this is not a homework
  5. Offline

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    I found 4) and 1) i need just a little hint for 2) and 3)
  6. Offline

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    again, what have you done so far?

    i have no idea what 2) is asking.
    hint for q3 = cosine rule
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    For 1)
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    (Original post by MAA_96)
    2)the length of the three medians of this triangle
    Start by finding the coordinates of the centroid...

    You should know what to do next.

    If not:

    Spoiler:
    Show

    Call the centroid I(a,b,c).

    Median from A:\;\dfrac{3}{2}AI

    Median from B:\;\dfrac{3}{2}BI

    Median from C:\;\dfrac{3}{2}CI
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    (Original post by z0tx)
    Start by finding the coordinates of the centroid...
    Do i have to use midpoint and use the distance formula or...to find that ?
  10. Offline

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    (Original post by MAA_96)
    Do i have to use midpoint and use the distance formula or...to find that ?
    Nope, midpoints would be a waste of time.

    The coordinates of the centroid are:

    I\left(\dfrac{1}{3}(x_a+x_b+x_c)  ,\dfrac{1}{3}(y_a+y_b+y_c), \dfrac{1}{3}(z_a+z_b+z_c)\right)

    Keep that in mind for future problems involving triangles!

    Also, in case you don't know: the median is 3/2 of the distance between the vertex in question and the centroid.
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    I should that yes, you could find the three midpoints and calculate the three distances, but why do something thrice when you can do it once?
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    Nice,but why did you choose centroid here?
  13. Offline

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    (Original post by MAA_96)
    Nice,but why did you choose centroid here?
    I just told you. Finding the centroid (i.e. a single point) is quicker than finding all the midpoints (i.e. three points).
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    Alright,thank you.

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