Question

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: Identify coordinates of D and E

Point D is at -4, point E is at 5.

Step2: Use section formula

The section formula for a point dividing a line segment from \((x_1,y_1)\) to \((x_2,y_2)\) in ratio \(m:n\) is \(x=\frac{mx_2 + nx_1}{m + n}\). Here, \(m = 4\), \(n = 5\), \(x_1=-4\), \(x_2 = 5\).

$$x=\frac{4\times5+5\times(-4)}{4 + 5}$$

Step3: Calculate numerator and denominator

Numerator: \(4\times5+5\times(-4)=20 - 20 = 0\)
Denominator: \(4 + 5 = 9\)

$$x=\frac{0}{9}=0$$

Answer:

0