Question

what is the location of point g, which partitions the directed line segment from d to f into a 5:4 ratio?
d is at -2, f is at 7.
options: -1, 0, 2, 3

Explanation:

Step1: Identify coordinates of D and F

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

Step2: Apply section formula

The formula for a point \( G \) that divides the line segment joining \( (x_1,y_1) \) and \( (x_2,y_2) \) in the ratio \( m:n \) is \( G = \frac{mx_2 + nx_1}{m + n} \). Here, \( x_1 = -2 \), \( x_2 = 7 \), \( m = 5 \), \( n = 4 \).

Step3: Substitute values

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

Answer:

3