Question

Draw a line, 8 centimetres long and divide it into five equal parts.

Answer 1

The steps of construction to divide a line segment of length 8 cm into five equal parts, i.e., in the ratio 1:1:1:1:1 are as follows:

1) Draw a line segment AB of length 8 cm.

2) Draw an acute angle, ∠YAB, at point A on the upper side of AB such that AY = 5 cm (sum of ratios).

3) Mark a point X₁ on AY at a distance of 1 cm from A.

4) Mark a point X₂ on AY at a distance of 1 cm from X₁.

5) Mark a point X₃ on AY at a distance of 1 cm from X₂.

6) Mark a point X₄ on AY at a distance of 1 cm from X₃. The remaining length X₄Y = 5 cm − 1 cm − 1 cm − 1 cm − 1 cm = 1 cm.

7) Join YB and draw line segments X₁C, X₂D, X₃E and X₄F parallel to YB.

We have obtained that AC:CD:DE:E :FB = 1:1:1:1:1

Thus, points C, D, E and F divide line segment AB of length 8 cm into five equal parts.