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Home > Geometry > Coordinate Geometry > Show that the points are collinear example
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Determine if the points A(0,0), B(2,0), C(-4,0), D(-2,0) are collinear points example
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- A(-1,-1), B(1,5), C(2,8), Find points are collinear points or triangle
- Determine if the points A(1,5), B(2,3), C(-2,-11) are collinear points
- Show that the points A(-3,0), B(1,-3), C(4,1) are vertices of a right angle triangle
- Show that the points A(1,1), B(-1,-1), C(-1.732051,1.732051) are vertices of an equilateral triangle
- Show that the points A(7,10), B(-2,5), C(3,-4) are vertices of an isosceles triangle
- Determine if the points A(0,0), B(2,0), C(-4,0), D(-2,0) are collinear points
- Show that the points A(1,2), B(5,4), C(3,8), D(-1,6) are vertices of a square
- Show that the points A(-4,-1), B(-2,-4), C(4,0), D(2,3) are vertices of a rectangle
- Show that the points A(3,0), B(4,5), C(-1,4), D(-2,-1) are vertices of a rhombus
- Show that the points A(-3,-2), B(5,-2), C(9,3), D(1,3) are vertices of a parallelogram
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6. Determine if the points A(0,0), B(2,0), C(-4,0), D(-2,0) are collinear points
1. 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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