Measuring Line Segments
A line segment is a part of a line with two fixed endpoints. Unlike a line (which goes on forever), a line segment has a definite length that you can measure.
In daily life, you measure many things — the length of your pencil, the width of your notebook, the height of a table. All of these are line segments.
In Class 6 NCERT Maths, you will learn different ways to measure and compare line segments using a ruler, a divider, and a compass.
What is Measuring Line Segments - Grade 6 Maths (Understanding Elementary Shapes)?
Definition: A line segment is the shortest path between two points. It has a fixed length.
A line segment with endpoints A and B is written as AB (with a bar on top in textbooks). Its length is written as AB (without the bar) and is measured in units like cm or mm.
Methods to measure a line segment:
- Method 1: Using a ruler (most common)
- Method 2: Using a divider (more accurate)
- Method 3: Using a ruler and compass
Measuring Line Segments Formula
Method 1: Measuring with a ruler
- Place the ruler along the line segment.
- Align the 0 mark of the ruler with one endpoint.
- Read the number at the other endpoint. That is the length.
Method 2: Measuring with a divider
- Open the divider and place each pointed tip on one endpoint of the line segment.
- Without changing the opening, place the divider on the ruler.
- Place one tip at 0 and read the number at the other tip.
Comparing line segments:
- By observation: Just look — this works only if the difference is obvious.
- By tracing: Trace one segment on paper and place it on the other.
- By measurement: Measure both using a ruler. The longer one has a greater measurement. This is the most reliable method.
Types and Properties
- Centimetre (cm) is the most common unit for small lengths.
- Millimetre (mm) is used for very small lengths. 1 cm = 10 mm.
- Metre (m) is used for longer lengths. 1 m = 100 cm.
Reading a ruler:
- The big numbered markings on a ruler are centimetres.
- The small markings between them are millimetres.
- There are 10 small markings (mm) between each cm marking.
- A reading like 5.7 cm means 5 cm and 7 mm.
Solved Examples
Example 1: Measuring a Line Segment with a Ruler
Problem: A line segment PQ has one end at the 0 mark and the other end at the 6.3 cm mark on a ruler. What is the length of PQ?
Solution:
Length = 6.3 cm − 0 cm = 6.3 cm
Answer: PQ = 6.3 cm
Example 2: Measuring When Not Starting from Zero
Problem: A line segment has one end at the 2.5 cm mark and the other at the 8.1 cm mark. Find its length.
Solution:
Length = 8.1 − 2.5 = 5.6 cm
Answer: The length is 5.6 cm
Note: You do not have to start from 0. Just subtract the two readings.
Example 3: Comparing Two Line Segments
Problem: Line segment AB = 7.4 cm and line segment CD = 5.9 cm. Which is longer? By how much?
Solution:
7.4 cm > 5.9 cm, so AB is longer.
Difference = 7.4 − 5.9 = 1.5 cm
Answer: AB is longer than CD by 1.5 cm.
Example 4: Converting mm to cm
Problem: A line segment is 45 mm long. What is its length in cm?
Solution:
1 cm = 10 mm, so 45 mm = 45/10 = 4.5 cm
Answer: 4.5 cm
Example 5: Adding Line Segments
Problem: Point B lies on line segment AC. AB = 3.2 cm and BC = 4.5 cm. Find AC.
Solution:
Since B is between A and C: AC = AB + BC = 3.2 + 4.5 = 7.7 cm
Answer: AC = 7.7 cm
Example 6: Finding an Unknown Part
Problem: Line segment PQ = 10 cm. Point R lies on PQ such that PR = 6.3 cm. Find RQ.
Solution:
PQ = PR + RQ
10 = 6.3 + RQ
RQ = 10 − 6.3 = 3.7 cm
Answer: RQ = 3.7 cm
Example 7: Drawing a Line Segment of Given Length
Problem: Draw a line segment of length 5.8 cm.
Solution:
- Place the ruler on the paper.
- Mark a point at the 0 cm mark. Call it A.
- Mark another point at the 5.8 cm mark. Call it B.
- Join A and B using the ruler's edge.
Answer: Line segment AB = 5.8 cm.
Example 8: Perimeter Using Line Segments
Problem: A triangle has sides measuring 4.2 cm, 5.1 cm, and 3.7 cm. Find its perimeter.
Solution:
Perimeter = sum of all sides = 4.2 + 5.1 + 3.7 = 13.0 cm
Answer: The perimeter is 13 cm.
Real-World Applications
Where measuring line segments is used:
- Construction: Builders measure lengths of walls, beams, and pipes.
- Tailoring: A tailor measures cloth lengths for stitching clothes.
- Drawing: In geometry class, you draw line segments of specific lengths for constructions.
- Maps: Distances on maps are represented as line segments. A scale converts map distance to real distance.
- Furniture: The dimensions of a table, shelf, or bed are all line segment measurements.
Key Points to Remember
- A line segment has two endpoints and a definite, measurable length.
- Measurement can be done using a ruler, divider, or compass.
- When measuring with a ruler, align one endpoint with 0 and read the other endpoint.
- If not starting from 0, subtract the two readings.
- 1 cm = 10 mm and 1 m = 100 cm.
- A divider is more accurate than a ruler because there are no parallax errors.
- If a point lies between two endpoints, the total length equals the sum of the two parts.
- Always write the unit (cm, mm, or m) with the measurement.
Practice Problems
- Measure the length of your pencil using a ruler.
- Draw a line segment of length 7.3 cm.
- A line segment has endpoints at the 3.2 cm and 9.8 cm marks on a ruler. Find its length.
- Point M lies on segment XY such that XM = 4.5 cm and MY = 3.5 cm. Find XY.
- Convert 72 mm to cm.
- Compare: AB = 5.6 cm and CD = 56 mm. Are they equal?
Frequently Asked Questions
Q1. What is a line segment?
A line segment is a part of a line with two fixed endpoints. It has a definite length that can be measured. For example, the edge of a book is a line segment.
Q2. How is a line segment different from a line?
A line goes on forever in both directions and has no fixed length. A line segment has two endpoints and a fixed, measurable length.
Q3. Why is a divider more accurate than a ruler?
With a ruler, the markings may be slightly inside the edge, causing parallax errors. A divider picks up the exact endpoints of the segment and transfers them to the ruler, giving a more accurate reading.
Q4. What if my line segment does not start at 0 on the ruler?
Subtract the smaller reading from the larger reading. For example, if the ends are at 2.3 cm and 7.8 cm, the length is 7.8 − 2.3 = 5.5 cm.
Q5. How many mm are in 1 cm?
There are 10 mm in 1 cm. So 1 cm = 10 mm, and to convert mm to cm, divide by 10.
Q6. What does 5.7 cm mean on a ruler?
It means 5 cm and 7 mm. The number before the decimal is cm, and the number after is mm (tenths of a cm).
