Question

Amar travels $1$ km due East, then $5$ km due South, then $2$ km due East and finally $9$ km due North. How far is from the starting point ?

• A. $16$ km
• B. $8$ km
• C. $6$ km
• D. $5$ km

Answer 1

Answer: (D)

$5$ km

Suppose Amar starts travelling from origin.

He travels 1 km East, then 5 km South, then 2 km East and finally 9 km North.

So, he makes a right angle triangle ABC from origin with base BC $=4$ km and side AB $=3$ km.

$\therefore$ by Pythagoras Theorem,

AB${}^2+$ BC${}^2=$ AC${}^2$.

$3^2+4^2=$ AC${}^2$

$\therefore$ AC$=5$ km.

Hence, Amar is $5$ km far from the starting point.