Question

what is the location of point f, which partitions the directed line segment from d to e into a 5:6 ratio? options: $\frac{-1}{11}$, $\frac{1}{11}$, $\frac{2}{15}$, $\frac{15}{2}$

Explanation:

Step1: Identify coordinates of D and E

From the number line, \( D = -4 \) and \( E = 5 \). The ratio \( m:n = 5:6 \).

Step2: Use section formula

The formula for a point \( F \) that divides the line segment from \( D(x_1) \) to \( E(x_2) \) in ratio \( m:n \) is \( F=\frac{mx_2 + nx_1}{m + n} \).

Substitute \( x_1=-4 \), \( x_2 = 5 \), \( m = 5 \), \( n = 6 \):

\( F=\frac{5\times5+6\times(-4)}{5 + 6}=\frac{25-24}{11}=\frac{1}{11} \)

Answer:

\(\frac{1}{11}\) (corresponding to the option with \(\frac{1}{11}\))