Question

Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3. Also, justify your construction.

Answer 1

Step-by-step explanation:

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Answer 2

Steps for construction:

1. Draw a line segment AB = 12 CM

2. Through the points A and B draw two parallel lines on the opposite sides of AB.

3. Cut three equal parts on BY and two equal parts on AX such that AA₁ = A₁A₂ and BB₁ = B₁B₂ = B₂B₃.

4. Join A₂B₃ which intersects AB at P.

Therefore by construction AB/BP = 2/3

Justification:

1. In ΔAA₂P and ΔBB₃P, We have

∠APA₂​=∠BPB₃ (because they are vertically opposite angles)

∠A₂AP=∠B₃BP (Alternate interior angles are equal)

△AA₂P and △BB₃​P are similar to each other (Angle Angle similarity)

Therefore AP/BP =AA₂/BB₃ =2/3