Question

In Figure $1$, the ratio of $AB$ to $BC$ is $7:5$. If $AC=1$, calculate the distance from $A$ to the midpoint of $BC$.

• A. $\frac{5}{8}$
• B. $\frac{2}{3}$
• C. $\frac{19}{24}$
• D. $\frac{3}{4}$

Answer 1

Answer: (C)

$\frac{19}{24}$

Given $AC=1$

Ratio of $AB$ to $BC$ is $7:5$, which implies

$AB=\frac{7}{12}$ and $BC=\frac{5}{12}$

Distance from $A$ to midpoint of $BC$ is $AB+\frac{BC}{2}=\frac{7}{12}+\frac{5}{24}=\frac{19}{24}$