Question

Drek traveled through Atlanta, Boston, Chicago, and Denver (A, B, C, and D) successively on a map as given:

What distance did he cover from C to D?

• A. 25 miles
• B. 12.5 miles
• C. 20 miles
• D. 12 miles

Answer 1

The correct option is B 12.5 miles

If we draw the entire journey from points A to D and join them, a right-angled triangle.

We can apply the Pythagoras theorem to calculate the length of AC.
According to the theorem,

${\left(\mathrm{AC}\right)}^2={\left(\mathrm{BC}\right)}^2+{\left(\mathrm{AB}\right)}^2\mathrm{BC}=7\mathrm{miles}\mathrm{AB}=24\mathrm{miles}{\left(\mathrm{AC}\right)}^2={\left(7\right)}^2+{\left(24\right)}^2{\left(\mathrm{AC}\right)}^2=49+576{\left(\mathrm{AC}\right)}^2=625\mathrm{AC}=\sqrt{625}\mathrm{AC}=25\mathrm{miles}$

His final position is the midpoint of AC.
Hence,

$\mathrm{CD}=\frac{\mathrm{AC}}{2}\mathrm{CD}=\frac{25}{2}\mathrm{CD}=12.5m$

Drek traveled 12.5 m from point C to reach D.