Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 3 with A(6, -10) and B(9, -1).

Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 3 with A(6, -10) and B(9, -1).

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  1. Answer:

    Step-by-step explanation:

    Use the formulas that allow us to find the point that divides the segment into a ratio which is

    [tex]x=\frac{bx_1+ax_2}{a+b}[/tex]  and  [tex]y=\frac{by_1+ay_2}{a+b}[/tex] where a is 1 (comes from the ratio) and b is 3 (comes from the ratio as well). Filling in:

    [tex]x=\frac{3(9)+1(6)}{1+3}=\frac{27+6}{4}=\frac{33}{4}[/tex] and then y:

    [tex]y=\frac{3(-1)+1(-10)}{1+3}=\frac{-3-10}{4}=-\frac{13}{4}[/tex] so the coordinates in question are

    [tex](\frac{33}{4},-\frac{13}{4})[/tex]

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