Question

To divide a line segment $AB$ in the ratio $5:6$, draw a ray $AX$ such that $\angle$ $BAX$ is an acute angle, then draw a ray $BY$ parallel to $AX$ and the points $A_1,A_2,A_3,$ ... and $B_1,B_2,B_3,$ ... are located at equal distances on ray $AX$ and $BY$, respectively. Then the points joined are ____

• A. $A_5$ and $B_6$
• B. $A_6$ and $B_5$
• C. $A_4$ and $B_5$
• D. $A_5$ and $B_4$

Answer 1

Answer: (A)

$A_5$ and $B_6$

The ratio is $5:6$

Therefore, total number of divisons on $BY$ and $AX$ is $5+6=11$.

$\Delta AOX$ and $BOY$ are similar, since $AX\parallel BY$

$\Rightarrow \angle X=Y$ and $\angle A=B$

$\therefore \frac{\text{no. of divisions on}B}{\text{no. of divisions on}A}=\frac{6}{5}$

$\Rightarrow$ number of divisions on $B$

$\Rightarrow$ number of divisions on $B=\frac{6}{5}\times$ number of divisions in $A$

$\Rightarrow \frac{6}{5}\times 5=6$

So, $A_5$ should be joined to $B_6$.