Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

math problem?

Let C(x,y) be a point between A(1,6) and B(−9,26) that is four times as far from A as it is from B. Find C(x,y)

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  • 4 weeks ago

    C = (1A+4B)/5 = ((1,6)+4(−9,26))/5 = (-35,110)/5 = (-7,22)

    Source(s): The point that partitions the line segment A to B into a ratio of a:b is (bA+aB)/(a+b).
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  • Philip
    Lv 6
    4 weeks ago

    In going from A(1,6) to B(-9,26) the following

    occurs: x falls 2 units 5 times.

    .............y rises 4 units 5 times.

    In order that C be 4 times as far from A that it is

    from B, x falls 4 times and y rises 4 times, ie.,

    x falls 8 units and y rises 16 units. Then, at C,

    x = (1-8) = -7 and y = 6+16 = 22. So we have

    C(-7,22).

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  • Pope
    Lv 7
    4 weeks ago

    Point C divides AB internally in ratio 4:1. This works like a weighted mean. Since B is the nearer point, it gets the greater weight, 4, while A gets weight 1.

    A(1, 6), B(-9, 26), C(x, y)

    x = [1(1) + 4(-9)] / (4 + 1) = -7

    y = [1(6) + 4(26)] / (4 + 1) = 22

    C(-7, 22)

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  • Imagine a line between A and B.  Divide that line into 5 parts.  5 because the segment between AC is 4 times as long as the segment between BC, so 4:1 =>> 4 + 1 = 5

    Now find the change in x and the change in y for each segment

    change in x per segment: (-9 - 1) / 5 = -10/5 = -2

    change in y per segment: (26 - 6) / 5 = 20/5 = 4

    Add 4 segments to each coordinate

    (1 + 4 * (-2) , 6 + 4 * 4) =>

    (1 - 8 , 6 + 16) =>

    (-7 , 22)

    The point is (-7 , 22)

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  • 4 weeks ago

    Let C(x, y) be a point between A(1, 6) and B(−9, 26) 

    that is four times as far from A as it is from B. 

    Then C(x, y) = C(-7, 16)

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