Understanding Line Segments and Their Measurements

Step-by-step Guide: Line Segments and Measurements

Line Segment:
A line segment is a part of a line that has two defined endpoints. Unlike lines that extend infinitely in both directions, a line segment has a distinct beginning and end. It comprises countless points, including its endpoints.

Example: Line segment \(AB\) is represented by the two endpoints \(A\) and \(B\).

Measurement of Line Segment:
The length of a line segment is a measure of the distance between its two endpoints. This measurement is typically done with the help of a ruler or a digital tool, depending on the context. The length is always a non-negative value and is commonly represented in units like centimeters, meters, inches, etc.

Example: If line segment \(CD\) measures \(5\) centimeters, we write it as \(CD = 5 \text{cm}\).

Examples

Example 1:

If you have a line segment \(EF\) with point \(G\) lying between \(E\) and \(F\), and \(EG = 2 \text{cm}\) while \(GF = 3 \text{cm}\), what is the length of line segment \(EF\)?

Solution:

The total length of line segment \(EF\) is the sum of \(EG\) and \(GF\).

Thus, \(EF = EG + GF\).

Given \(EG = 2 \text{cm}\) and \(GF = 3 \text{cm}\), \(EF = 2 \text{cm} + 3 \text{cm} = 5 \text{cm}\).

So, \(EF = 5 \text{cm}\).

Example 2:

Given a line segment \(HI\) of length \(8 \text{cm}\) and a point \(J\) lying on it such that \(HJ = 3 \text{cm}\), determine the length of segment \(JI\).

Solution:

To find \(JI\), subtract the length of \(HJ\) from \(HI\).

Given \(HI = 8 \text{cm}\) and \(HJ = 3 \text{cm}\), \(JI = HI – HJ\). \(JI = 8 \text{cm} – 3 \text{cm} = 5 \text{cm}\).

So, \(JI = 5 \text{cm}\).

Practice Questions:

1. If line segment \(KL\) is \(10 \text{cm}\) and \(KM\) is \(4 \text{cm}\), with \(M\) lying between \(K\) and \(L\), what is the length of \(ML\)?
2. Line segment \(VW\) is \(18 \text{cm}\). If \(VX\) is \(7 \text{cm}\) with \(X\) lying between \(V\) and \(W\), what is the length of \(XW\)?
3. Line segment \(EG\) is \(24 \text{cm}\). If point \(G\) divides \(EF\) such that \(FG = 9 \text{cm}\), determine the length of \(EF\).

Answers:

1. \(ML = 6 \text{cm}\), since the segment is the remainder after subtracting \(KM\) from \(KL\).
2. \(XW = 11 \text{cm}\), since the segment is the remainder after subtracting \(VX\) from \(VW\).
3. \(EF = 15 \text{cm}\), which is the sum of the total length of \(EG\) and segment \(FG\).