Split line segment AB at a ratio of 7 : 3

As GeoGebra allows us to calculate with vectors, this is an easy task.

    A = (-2, 1)
    B = (3, 3)
    T = A + 7/10 (B - A)

Another way of doing this could be

    A = (-2, 1)
    B = (3, 3)
    v = Vector[A, B]
    T = A + 7/10 v

In a next step we could introduce a number t (e.g. by using a slider, 3.2.10) and redefine the point T as T = A + t v (see 3.1.7). By changing t you can see T moving along a straight line.

This line could be entered now in parameter form (see 4.2.3):

    g: X = T + s v