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  1. #1
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    Exclamation geometry

    i need help with a question ...
    ΔPQR has vertices P(1, 3), Q(-1, 1), and R(5, 1). Determine the coordinates of the centroid of ΔABC.

    What goes centroid mean and how do you solve it!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by sunnyyueliang View Post
    i need help with a question ...
    ΔPQR has vertices P(1, 3), Q(-1, 1), and R(5, 1). Determine the coordinates of the centroid of ΔABC.

    What goes centroid mean and how do you solve it!
    Centroid means center.

    Triangle Centroid -- from Wolfram MathWorld
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  3. #3
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    it is the center of the triangle.

    find the midpoint of all the segments. the point of intersection of lines formed from each vertex to the midpoint of each opposite segment is the centroid.
    hope that helps!
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  4. #4
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    Don't get the centroid mixed up with the incenter.
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  5. #5
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    centroid is located at intersection of medians where as the incenter is located at intersection of the angle bisectors
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  6. #6
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    Quote Originally Posted by sunnyyueliang View Post
    i need help with a question ...
    ΔPQR has vertices P(1, 3), Q(-1, 1), and R(5, 1). Determine the coordinates of the centroid of ΔABC.

    What goes centroid mean and how do you solve it!
    If you know the coordinates of the vertices then the coordinates of the centroid are calculated by a simple formula:

    If P(x_P, y_P), Q(x_Q, y_Q) and R(x_R, y_R) then the centroid

    C\left(\dfrac13(x_P + x_Q + x_R)\ ,\  \dfrac13(y_P + y_Q + y_R)\right)

    With your question: C\left(\dfrac53\ ,\ \dfrac53 \right)
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  7. #7
    Member alunw's Avatar
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    There is no such thing as "the" center of a general triangle. A triangle has many different kinds of center just as a collection of numbers has many different kinds of average. There is a very extensive online encycolpedia about triangle centers here:
    ENCYCLOPEDIA OF TRIANGLE CENTERS
    The formulas it gives use either trilinear or barycentric coordinates which are both quite different from ordinary Cartesian coordinates.
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