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by Anonymous on June 18th, 2009

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How do you find out if 3 points are collinear without graphing them?

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  • by calicorey on June 18th, 2009

    calicorey

    Use the slope formula. If the difference of the y's divided by the difference of the x's is the same for two pairs of points, then they are collinear.

    examples:
    (2,5) (0,1) (15,31)

    First pair: (5-1)/(2-0) = 4/2=2
    Second pair: (1-31)/(0-15)=-30/-15=2
    Both pairs have the same slope, so the lines are collinear
    (You can also use the third pair: (31-5)/(15-2)=26/13=2)


    Contra-example:
    (-1,1), (-2,2), (-3,0)
    First pair: (1-2)/(-1+2)=-1/1=-1
    Second pair: (2-0)/(-2+3)=2/1=2
    If you connect the dots of the first pair, the line has a slope of -1. If you connect the dots of the second pair, the line has a slope of 2. These points can't be collinear.

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