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Constructions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsConstructions1 Mark
MCQ
Choose the correct answer from the given four options.
To divide a line segment $A B$ in the ratio $5: 6$, draw a ray $A X$ such that $\angle B A X$ is an acute angle, then draw a ray $B Y$ parallel to $A X$ and the points $A_1, A_2, A_3, \ldots$ and $B_1, B_2, B_3, \ldots$ are located at equal distances on ray $A X$ and $B Y$, respectively. Then the points joined are:
  • ✓
    $A _5$ and $B _6$
     
  • B
    $A _6$ and $B _5$
     
  • C
    $A _4$ and $B _5$
     
  • D
    $A _5$ and $B _4$
✓

Answer

Correct option: A.
$A _5$ and $B _6$
 

Given a line segment $AB$ and we have to divide it in the ratio $5 : 6.$

Steps of construction:
$1.$ Draw a ray $AX$ making an acute $\angle BAX$.
$2.$ Draw a ray $BY$ parallel to $AX$ by making $\angle ABY$ equal to $\angle BAX$.
$3.$ Now, locate the points $A_1, A_2, A_3, A_4$ and $A_5(m=5)$ on $A X$ and $B_1, B_2, B_3, B_4, B_5$ and $B_6(n=6)$
such that all the points are at equal distance from each other.
$4.$ Join $B_6 A_5$. Let it intersect $A B$ at a point $C$.
Then, $A C: B C=5: 6$

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