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 5.
a - 27
b?
c - 9

Explanation:

Step1: Use the section - formula

Let \(A=-27\), \(C = - 9\), and the ratio \(m:n=1:5\). The formula for a point \(B\) that divides the line - segment joining \(A\) and \(C\) in the ratio \(m:n\) is \(B=\frac{mA + nC}{m + n}\).

Step2: Substitute the values

Substitute \(m = 1\), \(n = 5\), \(A=-27\), and \(C=-9\) into the formula:
\[

$$\begin{align*} B&=\frac{1\times(-27)+5\times(-9)}{1 + 5}\\ &=\frac{-27-45}{6}\\ &=\frac{-72}{6}\\ &=-12 \end{align*}$$

\]

Answer:

\(-12\)