The endpoints of AB are A (-4,8) and B (12,-4). How do you find the coordinates of P if P lies on AB and is 3/8 the distance from A to B?

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Winston Cooper · Accepted Answer

Assuming the point P lies on the line AB such that      P    A    :    P    B    =    3    :    8    ≡    m    :    n  point P internally divides the line AB with end points       A          (      -      4      ,      8      )        ≡          (              x        1            ,              y        1            )       &amp;amp;       B          (      12      ,      -      4      )        ≡          (              x        2            ,              y        2            )      The coordinates of point P are given by internal division formula as follows            (                        m                      x            2                    +          n                      x            1                                    m          +          n                    ,                        m                      y            2                    +          n                      y            1                                    m          +          n                    )            ≡          (                        3          ⋅          12          +          8                      (            -            4            )                                    3          +          8                    ,                        3                      (            -            4            )                    +          8                      (            8            )                                    3          +          8                    )            ≡          (                        4                          11                    ,                        52                          11                    )

The endpoints of AB are A (-4,8) and B (12,-4). How do you find the coordinates of P if P lies on AB and is 3/8 the distance from A to B?

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