Draw a line segment of length 7 cm.


Draw a line segment of length 7 cm. Find a point P on it which1 divides it in the ratio 3:5.


Steps of construction

  1. Draw a line segment AB = 7 cm.
  2. Draw a ray AX, making an acute ∠BAX
  3. Along AX, mark 3+ 5= 8 points
    A1, A2, A3, A4, A5, A6, A7, A8 such that
    AA= A1A= A2A3 = A 3A4 = A 4A5 = A 5A6 = A 6= A 7A8
  4. Join   A8B             
  5. From A3, draw A3C || A8B meeting AB at C.
    [by making an angle equal to ∠BA 8A at A 3]

Then, C is the point on AB which divides it in the ratio 3 : 5,

$\therefore$ $\frac{A C}{C B}=\frac{A A_{3}}{A_{3} A_{8}}=\frac{3 x}{5 x}=\frac{3}{5}$

Hence, $A C: C B=3: 5$


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