Question

Draw a line segment $PQ=10$ cm, Take a point $A$ on $PQ$ such that $PA:PQ=2:5$. Measure the length of $PA$ and $AQ$.

Answer 1

(1) Draw a line segment of length PQ=10cm.

(2) Draw any ray PX making an acute angle $\angle QPX$ with PQ.

(3) Draw a parallel line to PX by making $\angle PQY=\angle QPX$

(4) Mark two points $C_1,C_2$ on PX and 3 ponts $B_1,B_2,B_3$ such that $P{C}_1={C_{1}C}_2$

$Q{B}_1=B_1{B}_2=B_2{B}_3$

(5) Join $C_2$ to $B_3$. Then it intersect PQ at point A. Thus A is the point of dividing PQ such $\frac{PA}{PQ}=\frac{2}{5}$ or $\frac{PA}{QA}=\frac{2}{3}$

The length of PA=4cm and QA=6cm.