Question

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. [4 Marks]

Answer 1

1) Draw a line segment AB = 7.6 cm. [0.5 Mark]

2) Draw a ray AX making an acute angle $\angle$ BAX along with AB. [0.5 Mark]

3) On AX make 5 + 8 i.e. 13 equal parts and mark them as $A_1,A_2,A_3,A_4,...A_{13}$ [1 Mark]

4) Join B to $A_{13}$. From $A_5$ draw $A_{5}C\parallel A_{13}B$.

C is the required point of division and AC: CB = 5 : 8.

On measuring, we get

AC = 3.1 cm,

CB = 4.5 cm

Justification

$A_{5}C\parallel A_{13}B$

$\frac{A_{5}C}{A_5{A}_{13}}=\frac{AC}{CB}$

[Using basic proportionality theorem]

But $\frac{A_{5}C}{A_5{A}_{13}}=\frac{5}{8}$

This shows that C divides AB in the ratio 5 : 8. [2 Marks]