Draw a line, 8 centimetres long and divide it in the ratio 4 : 5.

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Solution

The steps of construction to divide a line segment of length 8 cm in the ratio 4:5 are as follows:

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

2) At B, draw BY perpendicular to AB.

3) Taking A as the centre and 9 cm (sum of ratios) as the radius, draw an arc on BY. The point where the arc cuts BY is named as Q. Join AQ.

4) Taking A as the centre and 4 cm as the radius, draw an arc on AQ and name it as P. The remaining length XY = 9 cm − 4 cm = 5 cm.

5) Draw PC parallel to QB.

We have obtained that AC:CB = 4:5.

Thus, point C divides line segment AB of length 8 cm in the ratio 4:5.

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