Question

what is the location of point g, which partitions the directed line segment from d to f into a 5 : 4 ratio?

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

-1
0
2
3

Explanation:

Step1: Identify coordinates of D and F

From the number line, \( D \) is at \( -2 \) and \( F \) is at \( 7 \). The ratio is \( 5:4 \), so \( m = 5 \), \( n = 4 \).

Step2: Apply section formula

The section formula for a point \( G \) dividing \( \overline{DF} \) in ratio \( m:n \) is \( G=\frac{m\times F + n\times D}{m + n} \).
Substitute \( m = 5 \), \( n = 4 \), \( D=-2 \), \( F = 7 \):

$$ G=\frac{5\times7 + 4\times(-2)}{5 + 4}=\frac{35-8}{9}=\frac{27}{9}=3 $$

Answer:

3