Given the points J(-4,0) and K(0, 4), find the coordinates of the point P on directed line segment JK that partitions segment JK in th

Question

Given the points J(-4,0) and K(0, 4), find the coordinates of the point P on directed
line segment JK that partitions segment JK in the ratio 3:1

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Huyền Thanh 6 months 2021-08-25T11:57:11+00:00 1 Answers 0 views 0

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    2021-08-25T11:58:19+00:00

    Answer:

    Step-by-step explanation:

    We are given a ratio for this problem so we will use the formula for when we are given a ratio (as opposed to the formula for when you are given that the point you’re looking for is a fraction of the way from one point to another, like 1/3 of the way from point A to point B. That’s a different formula).

    The formulas are for the x and y coordinates of the point in question:

    x=\frac{bx_1+ax_2}{a+b}   and   y=\frac{by_1+ay_2}{a+b} where

    a = 3 (from the ratio),

    b = 1 (from the ratio),

    x1 = -4, y1 = 0 (from point J)

    x2 = 0, y2 = 4 (from point K). Filling in for x first:

    x=\frac{1(-4)+3(0)}{3+1} gives us

    x=\frac{-4}{4}=-1 and now for y:

    y=\frac{1(0)+3(4)}{3+1} gives us

    y=\frac{12}{4}=3

    Therefore, the coordinates that partition that segment into the ratio of 3:1 are (-1, 3)

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