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 6. location of b :

Explanation:

Step1: Identify the formula for dividing a line - segment

The formula to find the point $B(x)$ that divides the line - segment joining $A(x_1)$ and $C(x_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$. Here, $x_1=-29$, $x_2=-15$, $m = 1$, and $n = 6$.

Step2: Substitute the values into the formula

$x=\frac{1\times(-15)+6\times(-29)}{1 + 6}=\frac{-15-174}{7}=\frac{-189}{7}$.

Step3: Calculate the value

$\frac{-189}{7}=-27$.

Answer:

$-27$