Question

(i) Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5. [CBSE 2017]
(ii) Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

Answer 1

(i) Steps of Construction:

Step 1. Draw a line segment AB = 8 cm

Step 2. Draw a ray AX, making an acute angle $\angle$BAX.

Step 3. Along AX, mark (4 + 5 =) 9 points A₁, A₂, A₃, A₄, A₅, A₆, A₇, A₈ and A9 such that

AA₁ = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅ = A₅A₆ = A₆A₇ = A₇A₈ = A₈A₉

Step 4. Join A₉B.

Step 5. From A₄, draw A₄D parallel to A₉B (draw an angle equal to $\angle$AA₉B), meeting AB in D.



Here, D is the point on AB which divides it in the ratio 4 : 5.


(ii) Steps of Construction:

Step 1. Draw a line segment AB = 7.6 cm

Step 2. Draw a ray AX, making an acute angle $\angle$BAX.

Step 3. Along AX, mark (5 + 8 =) 13 points A₁, A₂, A₃, A₄, A₅, A₆, A₇, A₈, A₉, A₁₀, A₁₁, A₁₂ and A₁₃ such that

AA₁ = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅ = A₅A₆ = A₆A₇ = A₇A₈ = A₈A₉ = A₉A₁₀ = A₁₀A₁₁ = A₁₁A₁₂ = A₁₂A₁₃

Step 4. Join A₁₃B.

Step 5. From A₅, draw A₅P parallel to A₁₃B (draw an angle equal to $\angle$AA₁₃B), meeting AB in P.



Here, P is the point on AB which divides it in the ratio 5 : 8.

∴ Length of AP = 2.9 cm (Approx)

Length of BP = 4.7 cm (Approx)