The location of point G which partitions the directed line segment from D to F into a 5:4 ratio is; x = 3
Division of a Line Segment
The formula for coordinate of a point that divides a line segment in a ration is given by;
x = (mx₂ + nx₁)/(m + n)
We are given the ratio 5:4
Thus m = 5 and n = 4
The endpoints of DF are D(-2) and F(7)
Thus;
x = ((5*7) + 4(-2))/(5 + 4)
x = 27/9
x = 3
Thus, the location of point G which partitions the directed line segment from D to F into a 5:4 ratio is x = 3
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