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Analytic geometry - One dimensional coordinate system

Point cordinates : \(x_0,x_1,x_2,y_0,y_0,y_1,y_2\)

Real number : \(\lambda\)

Distance Between two Points : d

  1. Distance Between Twwo Points 
    \(d=AB=|x_2-x_1|=|x_1-x_2|\)

  2. Dividing a Line Segment in the Ration \(\lambda\)
    \(x_0={ x_1+\lambda x_2 \over 1+ \lambda } , \lambda={AC \over CB }, \lambda \ne -1\)


  3. Midpoint of a Line Segment 
    \(x_0= {x_1+x_2 \over 2}, \lambda=1 .\)