Question

a segment ab is partitioned as shown. complete the statement. the ratio of \\(\frac{ar}{ab}\\) is

Explanation:

Step1: Count the number of sub - segments

Let's assume each small segment between consecutive points has a length of 1 unit. Count the number of segments from A to R and from A to B. From A to R, there are 3 segments (AP, PL, LR). From A to B, there are 7 segments (AP, PL, LR, RM, MG, GS, SB).

Step2: Calculate the ratio

The ratio of $\frac{AR}{AB}$ is the number of segments from A to R divided by the number of segments from A to B. So, $\frac{AR}{AB}=\frac{3}{7}$.

Answer:

$\frac{3}{7}$