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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