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 4 to 5. location of b:

Explanation:

Step1: Calculate the total distance from A to C

The distance from $A=-25$ to $C = 11$ is $d=11-(-25)=11 + 25=36$.

Step2: Divide the distance according to the ratio

The ratio of $AB$ to $BC$ is $4$ to $5$, so the total number of parts is $4 + 5=9$ parts. Each part has a length of $\frac{36}{9}=4$.

Step3: Find the distance from A to B

Since $AB$ is $4$ parts, the distance from $A$ to $B$ is $4\times4 = 16$.

Step4: Calculate the location of B

Starting from $A=-25$, moving $16$ units to the right, we get $B=-25 + 16=-9$.

Answer:

$-9$