GEOMETRY MIDPOINT FORMULA steve how did this hapn

If a line is extended from A (2,3) through B ( -2, 0 ) to a point so that AC = 4ab Find the coordinates of C

Please help thanks so much
GEOMETRY MIDPOINT FORMULA - Steve, Thursday, January 30, 2014 at 11:58am
B-A = (-4,-3)
C-A = 4(B-A) = (-16,-12)
C = A+(C-A) = (-14,-9)

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asked by Joy
  1. looks like Steve was using vector geometry

    Perhaps the following approach might make sense to you:

    make a sketch.
    since AC = 4AB
    AB : BC = 1 : 3

    for the x's :
    (2 - (-2))/(-2-x) = 1/3
    12 = -2-x
    x = -14

    for the y's:

    (3-0)/(0-y) = 1/3
    9 = -y
    y = -9

    so point C is (-14, -9)

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    posted by Reiny
  2. thank you reinyyyyy <3

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  3. Sorry to be obscure, Joy. It was sort an informal shortcut, so I could present the subtraction of x- and y-values both at once. If you look carefully at Reiny's calculations, you will see that the same subtractions show up in my pairs of numbers.

    The logic was: figure the differences in x and y going from A to B: B-A

    Multiply those differences by 4

    Add those scaled differences to the original values for A, and you get the values for C.

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    posted by Steve
  4. thankssssss steve :) <33

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  5. What formula did you use?

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    posted by KJ
  6. hello, how did you got the ratio AB : BC = 1:3 ? Im just a little confuse, please explain briefly with the fraction, thanks.

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