Question

partitioning a directed line segment
what is the location of point f which partitions the
directed line segment from d to e into a 4:5 ratio?
-3
0
1
4

Explanation:

Step1: Determine the coordinates of D and E

From the number - line, \(D=-4\) and \(E = 5\).

Step2: Use the section formula for a one - dimensional line segment

The formula for a point \(F\) that divides the line segment from \(D\) to \(E\) in the ratio \(m:n\) is \(F=\frac{m\times E + n\times D}{m + n}\). Here, \(m = 4\) and \(n=5\).
Substitute the values: \(F=\frac{4\times5+5\times(-4)}{4 + 5}=\frac{20-20}{9}=0\).

Answer:

B. 0