Question

Draw a line segment of length 6.5 cm and divide it into four equal parts, using ruler and compasses.

Answer 1

Steps of construction:

1. Draw a line segment AB = 6.5 cm.
2. With A and B as centres and radius more than `1/2` (AB), draw arcs one on each side of AB, these arcs cuts each other at E and F.
3. Join EF, which cuts AB at Q.
4. With centres A and Q and radius more than `1/2` AQ, draw arcs one on each side of AB, these arcs cuts each other at G and H.
5. Join GH, which cuts AB at P.
6. Similarly, with centres B and Q and radius more than `1/2` (BQ), draw arcs one on each side of AB, these arcs cuts each other at I and J.
7. Join IJ, which cuts AB at R.
8. Now, point P, Q and R divide the line segment AB in four equal parts. Thus AP = PQ = QR = RB.