Math

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Use the distance formula to determine whether the points lie on the same line.
(0,4),(7,-6),(-5,11).
I know the distance formula, but I don't see how that will help me find out if they lie on the same line.

  • Math -

    distance between (0,4) and (7,-6) = √(49+100) = √149
    distance between (7,-6) and (-5,11) = √(144+289) = √433
    distance between (0,4) and (-5,11) = √(25+49) = √74

    if they are collinear, then
    √74 + √149 = √433
    IS it ??

    √74 + √149 = 20.80888088
    √433 = 20.80865205
    difference is .000228

    had you simply graphed it, you would not have noticed the difference, but there is a difference, so the points are NOT collinear.

    check: slope of 1st segment = -10/7
    slope of another segment = 7/-5

    since -10/7 ≠ -7/5 , they are not collinear.
    (notice the slopes are close)
    -1.42857 vs -1.4 , angles are 55.0° vs 54.5°

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