Equation of a Line

Through Point along Vector

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Given points O and A, a vector u and a parameter t, you should be able to find an equation for the vector r in terms of O, A, u and t. In the construction above this has been done. The point P, which is the endpoint of r has also been created. If t could take on any real value, the point P could reach any point on the line l.

In the construction below you are given the objects O, A, u and t (there are other objects as well but their names are hidden). Using these four objects make vector/vectors and point/points to find a vector r as in the construction above. You can make new objects by using these commands:

w=Vector[<Start Point>,<End Point>]
w=u+v (where u and v are vectors that are already defined)
w=a*u (where a is a number and u is vector, both defined)

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Through Two Points

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Given three points O, A and B; and a parameter t, you should be able to find an equation for the vector r in terms of O, A, B and t. In the construction above this has been done. The point P, which is the endpoint of r has also been created. If t could take on any real value, the point P could reach any point on the line l.

In the construction below you are given the objects O, A, B and t (there are other objects as well but their names are hidden). Using these four objects make vector/vectors and point/points to find a vector r as in the construction above.

Load GeoGebra worksheet