$A$ cyclist travels a distance of $4\, km$ from $P$ to $Q$ and then moves a distance of $3\, km$ at a right angle to $PQ$. Find his resultant displacement graphically.

(N/A) Graphically,the path forms a right-angled triangle where the base is $4\, km$ and the perpendicular height is $3\, km$.
The resultant displacement is the hypotenuse of this triangle.
Using the Pythagorean theorem:
$S = \sqrt{(4\, km)^2 + (3\, km)^2}$
$S = \sqrt{16 + 9}\, km$
$S = \sqrt{25}\, km$
$S = 5\, km$
Thus,the resultant displacement is $5\, km$.