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 2 to 1. location of b

Explanation:

Step1: Calculate the total number of parts

The ratio of \(AB\) to \(BC\) is \(2:1\), so the total number of parts is \(2 + 1=3\) parts.

Step2: Find the distance between \(A\) and \(C\)

The distance between \(A(-16)\) and \(C(5)\) is \(d=\vert5-(-16)\vert=\vert5 + 16\vert = 21\).

Step3: Calculate the length of one part

Since the total distance \(AC = 21\) and there are \(3\) parts, the length of one part is \(\frac{21}{3}=7\).

Step4: Calculate the coordinate of \(B\)

Since \(AB\) is \(2\) parts, the distance from \(A\) to \(B\) is \(2\times7 = 14\). Starting from \(A(-16)\) and moving \(14\) units towards \(C\), we get \(B=-16+14=-2\).

Answer:

\(-2\)