Construct a line segment of 10 cm. Divide this line segment in the ratio 3:2. [2 MARKS]

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Solution

Concept : 1 Mark
Construction : 1 Mark

Here, the ratio $\frac{A C}{C B}$ = 3:2.

Therefore, the number of arcs to be cut is 3+2 = 5.

Here, C divides AB in the ratio 3:2.

Steps of construction:

1. Draw a line segment $A B$ of length 10 cm.

2. Draw a ray from $A X$ such that angle between $A X$ and $A B$ is acute.

3. Draw five arcs $A_{1}, A_{2}, A_{3}, A_{4}, A_{5}$ on AX such that $A A_{1} = A_{1} A_{2} = A_{2} A_{3} = A_{3} A_{4} = A_{4} A_{5}$ .

4. Join $A_{5}$ and $B$ .

5. Draw a line $A_{3} C$ parallel to $A_{5} B$ .

6. The point $C$ divided $A B$ in the ratio $3 : 2$ .

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