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Solution
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Solution provided by AtoZmath.com
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Determine if the points are Collinear points calculator
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 1. Determine if the points `A(0,0), B(2,0), C(-4,0), D(-2,0)` are collinear points
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Example1. Determine if the points `A(0,0), B(2,0), C(-4,0), D(-2,0)` are collinear pointsSolution:We know that the distance between the two points `(x_1,y_1)` and `(x_2,y_2)` is
`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)` The given points are `A(0,0),B(2,0),C(-4,0),D(-2,0)` `CD=sqrt((-2+4)^2+(0-0)^2)` `=sqrt((2)^2+(0)^2)` `=sqrt(4+0)` `=sqrt(4)` `:. CD=2` `DA=sqrt((0+2)^2+(0-0)^2)` `=sqrt((2)^2+(0)^2)` `=sqrt(4+0)` `=sqrt(4)` `:. DA=2` `AB=sqrt((2-0)^2+(0-0)^2)` `=sqrt((2)^2+(0)^2)` `=sqrt(4+0)` `=sqrt(4)` `:. AB=2` `CB=sqrt((2+4)^2+(0-0)^2)` `=sqrt((6)^2+(0)^2)` `=sqrt(36+0)` `=sqrt(36)` `:. CB=6` Here `CD+DA+AB=2+2+2=6=CB` `:.` C,D,A,B are collinear points  |
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