Question

in the figure below, b lies between a and c. find the location of b so that the ratio of ab to bc is 1 to 2. location of b:

Explanation:

Step1: Use the section - formula

If a point $B$ divides the line - segment joining $A(x_1)$ and $C(x_2)$ in the ratio $m:n$, the coordinate of $B$ is given by $x=\frac{mx_2+nx_1}{m + n}$. Here, $x_1=-38$, $x_2=-11$, $m = 1$, and $n = 2$.

Step2: Substitute the values into the formula

$x=\frac{1\times(-11)+2\times(-38)}{1 + 2}=\frac{-11-76}{3}$.

Step3: Simplify the expression

$\frac{-11 - 76}{3}=\frac{-87}{3}=-29$.

Answer:

$-29$