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Question
To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A1, A2, A3, ... and B1, B2, B3, ... are located at equal distances on ray AX and BY, respectively. Then the points joined are ______.
Options
A5 and B6
A6 and B5
A4 and B5
A5 and B4
Solution
To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A1, A2, A3, ... and B1, B2, B3, ... are located at equal distances on ray AX and BY, respectively. Then the points joined are `underlinebb(A_5 and B_6)`.
Explanation:
To divide line segment AB in the ratio 5 : 6.
Steps of construction:
- Draw a ray AX making an acute ∠BAX.
- Draw a ray BY parallel to AX by taking ∠ABY equal to ∠BAX.
- Divide AX into five (m = 5) equal parts AA1, A1A2, A2A3, A3A4 and A4A5
- Divide BY into six (n = 6) equal parts and BB1, B1B2, B2B3, B3B4, B4B5 and B5B6.
- Join B6 A5. Let it intersect AB at a point C. Then, AC : BC = 5 : 6
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