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

$D = -2$, $F = 7$

Step2: Use section formula for ratio $m:n=5:4$

The formula for a point dividing a segment from $x_1$ to $x_2$ in ratio $m:n$ is $\frac{mx_2 + nx_1}{m + n}$
Substitute values: $\frac{5\times7 + 4\times(-2)}{5 + 4}$

Step3: Calculate numerator and denominator

Numerator: $5\times7 + 4\times(-2) = 35 - 8 = 27$
Denominator: $5 + 4 = 9$

Step4: Compute final value

$\frac{27}{9} = 3$

Answer:

3