NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Problems and Solutions

Question 89

Q89. Draw a line segment of length 10 cm. Divide it into four equal parts. Measure each part.

Answer

Each part = 2.5 cm

Step-by-step Explanation (Very Simple)

1. Draw the line segment.
   • Take a ruler and draw a straight line.
   • Mark the ends as A and B so that AB = 10 cm.
2. Find the length of one equal part (by calculation).

   ( ext{Total length} = 10 ext{ cm} )

   ( ext{Number of equal parts} = 4 )

   ( ext{Length of one part} = dfrac{10 ext{ cm}}{4} )

   ( = 2.5 ext{ cm} )

   So, each part should be 2.5 cm long.

3. Method 1 (using only the ruler): mark every 2.5 cm.
   • Place the 0 mark of the ruler at point A.
   • Put small pencil marks at 2.5 cm, 5.0 cm, and 7.5 cm on the line.
   • Label those points as P (2.5), Q (5.0), and R (7.5).
   • Now the line is split as: AP, PQ, QR, RB.
4. Check each part by measuring.
   • Measure AP with the ruler: it should be 2.5 cm.
   • Measure PQ: 2.5 cm.
   • Measure QR: 2.5 cm.
   • Measure RB: 2.5 cm.

   ( AP = 2.5 ext{ cm} )

   ( PQ = 2.5 ext{ cm} )

   ( QR = 2.5 ext{ cm} )

   ( RB = 2.5 ext{ cm} )

5. (Optional) Method 2 — neat compass construction (no measuring 2.5 on the ruler):
   1. From A, draw a short ray AX making any small angle with AB.
   2. Open the compass to a small, comfortable width. On ray AX, step off four equal arcs to get points A₁, A₂, A₃, A₄ (all gaps equal).
   3. Join A₄ to B.
   4. Through A₁, A₂, and A₃, draw lines parallel to A₄B. These lines will cut AB at three points and divide it into four equal parts.

   By construction, all four pieces on AB are equal, so each is 2.5 cm.

Final Calculation (shown in small steps)