Question

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

Explanation:

Step1: Identify coordinates of D and E

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

Step2: Apply section formula

The formula for a point \( F \) dividing \( \overline{DE} \) in ratio \( m:n \) is \( F = \frac{m \cdot E + n \cdot D}{m + n} \).

Substitute \( m = 5 \), \( n = 6 \), \( D = -4 \), \( E = 5 \):

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

Answer:

\(\frac{1}{11}\)