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Math Help - 3 points on a line

  1. #1
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    3 points on a line

    Given points A(x1, y1) and B(x2, y2), I'm supposed to derive the coordinate of the point C
    which should be on the line AB (such that B is on the line segment AC), such that the distance CB is 0.5*distance AC. The point is to avoid the solution where C is on "the other side", such that A is between C and B. We should obtain the solution where B is between A and C.

    Thanks
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  2. #2
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    Quote Originally Posted by onako View Post
    Given points A(x1, y1) and B(x2, y2), I'm supposed to derive the coordinate of the point C
    which should be on the line AB (such that B is on the line segment AC), such that the distance CB is 0.5*distance AC. The point is to avoid the solution where C is on "the other side", such that A is between C and B. We should obtain the solution where B is between A and C.

    Thanks
    So in other words we want B to be the midpoint of A and C. I get C = (x_1 + 2(x_2-x_1), y_1 + 2(y_2-y_1)) = (2x_2 - x_1, 2y_2 - y_1).
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  3. #3
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    Thanks for the message. Actually, the distance BC should be equal 0.5*distance AB, so the point B is between A and C, but not really the midpoint. It would be good to express the coordinates with the variable 'percent'(this 0.5). ?
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  4. #4
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    Quote Originally Posted by onako View Post
    Thanks for the message. Actually, the distance BC should be equal 0.5*distance AB, so the point B is between A and C, but not really the midpoint. It would be good to express the coordinates with the variable 'percent'(this 0.5). ?
    In that case I get

    C = (x_1 + 1.5(x_2-x_1), y_1 + 1.5(y_2-y_1)) = (1.5x_2 - 0.5x_1,  1.5y_2 -  0.5y_1)

    In general

    C = (x_1 + (1+p)(x_2-x_1), y_1 + (1+p)(y_2-y_1))

    where length of BC is p times length of AB.
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    Thanks
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