Question

in the figure below, b lies between a and c. find the location of b so that ab is \\(\frac{4}{9}\\) of ac. number line: a at 8, b at ?, c at 26 location of b : \\(\square\\)

Explanation:

Step1: Calculate the length of AC

The coordinate of A is 8 and the coordinate of C is 26, so the length of AC is \( 26 - 8 = 18 \).

Step2: Calculate the length of AB

Since \( AB=\frac{4}{9} \) of \( AC \), then \( AB = \frac{4}{9}\times18 = 8 \).

Step3: Find the location of B

The location of A is 8, and \( AB = 8 \), so the location of B is \( 8 + 8 = 16 \).

Answer:

16