Question

In the segment shown in figure, the ratio of the lengths of $\overline{AB}$ to $\overline{AC}$ is $5:8$. If $x$ represents $AB$, find the midpoint of $\overline{AC}$ in terms of $x$.

• A. $4x$
• B. $\frac{4x}{5}$
• C. $\frac{8x}{5}$
• D. $\frac{5x}{2}$

Answer 1

The correct option is B $\frac{4x}{5}$

Given, length of $AB$ to $AC$ is $5:8$ and $AB=x$

Then $\frac{AB}{AC}=\frac{5}{8}$

$\Rightarrow 5AC=8AB$

$\Rightarrow AC=\frac{8}{5}AB$

But $AB=x$

$\therefore AC=\frac{8}{5}x$

Then mid point of $AC$ $=\frac{1}{2}\times \frac{8}{5}x=\frac{4}{5}x$.