Question

Draw a line segment PQ of length 7 cm. Mark a point R on it, such that l(PR) : l(RQ) = 4 : 1.

Answer 1

The seg PQ of length 7 cm can be divided in the ratio 4:1 in the following way.

Steps of Construction:
1. Draw a line segment PQ of length 7 cm.
2. Now, draw a ray PL making an acute angle with PQ and draw a ray QM parallel to PL by making $\angle$PQM equal to $\angle$QPL.
3. Locate 4 points P₁, P₂, P₃, and P₄ on PL and 1 point Q₁ on QM, such that PP₁ = P₁P₂ = P₂P₃ = P₃P₄ = QQ₁.
4. Now, join P₄ Q₁ that intersects PQ at R.

So, R is the point on PQ that divides the line segment PQ in the ratio 4:1.