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:

(i) Draw a line segment AB = 6.5 cm.

(ii) 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.

(iii) Join EF, which cuts AB at Q.

(iv) 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.

(v) Join GH, which cuts AB at P.

(vi) 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.

(vii) Join IJ, which cuts AB at R.

(viii) Now, point P, Q and R divide the line segment AB in four equal parts.

Thus AP = PQ = QR = RB.