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Question
Draw a line segment AB of length 10 cm and divide it internally in the ratio of 2:5 Justify the division of line segment AB.
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Solution
Steps of construction:
- Draw a line segment AB of length 10 cm.
- Draw a line AX making an acute angle with AB.
- Mark 7 points A1, A2, A3, ...... A7 along AX such that AA1 = A1A2 = A1A3 = ...... = A6A7.
- Join point B with point A7.
- Through the point A2, draw a line parallel to A7B by making an angle equal to ∠AA7B at A2. This line meets AB at a point P.
As a result, point P is necessary to divide line AB internally in the ratio of 2 : 5.
Justification: In ΔAA7B, A2P || A7B.
As a result of the basic proportionality theorem,
`(A A_2)/(A_2A_7) = (AP)/(PB)` .......(i)
By the above construction,
`(A A_2)/(A_2A_7) = 2/5` ......(ii)
By equations (i) and (ii),
`(AP)/(PB) = 2/5`
Thus, AP : PB = 2 : 5
As a result, P splits the line AB in the ratio 2 : 5.
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