Question

Draw a line segment AB of length 6.5 cm and divide it in the ratio 4 : 7. Measure each of the two parts.

Answer 1

Steps of Construction:

Step 1: Draw a line segment AB = 6.5 cm.

Step 2: Draw a ray AX, making an acute angle ∠BAX.

Step 3: Jong AX, mark (4 + 7) = 11 points A₁, A₂, A₃, A₄, A₅, A₆ A₇, A₈, A₉, A₁₀, A₁₁ such that AA₁ = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅ = A₅A₆ = A₆A₇ = A₇A₈ = A₈A₉ = A₉A₁₀ = A₁₀A₁₁.

Step 4: Join A₁₁B.

Step 5: From A₄, draw A₄C || A₁₁B, meeting AB at C.

Thus, C is the point on AB, which divides it in the ratio 4 : 7.

Thus, AC : CB = 4 : 7

From the figure,

AC = 2.36 cm

CB = 4.14 cm