# To divide a line segment AB in the ratio $4:7$, a ray AX is drawn first such that $\angle BAX$ is an acute angle and then points $A_{1},A_{2},A_{3}\cdots$ are located at equal distances on the ray AX and the point B is joined to:(A) A12                        (B) A11            (C) A10            (D) A9

Answers (1)

Answer(B) A11
Solution

Given: $\angle BAX$ is an acute angle
The required ratio is $4:7$
Let m = 4, n = 7
$m+n= 4+7= 11$

Steps of construction
1. Draw any ray AX making an acute angle with AB.
2. Locate 11 points on AX at equal distances   (because m + n = 11)
3. Join $A_{11}B$
4. Through the point A4 draw a line parallel to $A_{11}B$  intersecting AB at the point P.
Then $AP:PB= 4:7$

Hence point B is joined to A11.

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