Draw a line segment PQ of length 8cm. Find 1/4 PQ using compass.

Follow the steps shown below to construct the required part of line segment PQ;
STEP I: Draw a line segment PQ = 8 cm using ruler.
STEP II: Place the compass point on P and adjust the compass to just over half the line length.
STEP III: Without adjusting the compass width, draw an arc on each side of the line.
STEP IV: Without changing the compass width, repeat for the other end of the line.
STEP V: Draw a straight line between the two arc intersections.
STEP VI: This straight line is the perpendicular bisector of line PQ at M.
STEP VII: Similarly draw a perpendicular bisector of the line PM at intersecting the line PQ at L.

Therefore the length of PL = $\frac{1}{4}\left(\mathrm{PQ}\right)$