## Line Segment Problems: Example Exam Questions

There is a formula to calculate line segments in geometry. If we have the coordinates of the two endpoints, we can calculate the distance between the two points. The formula to calculate the length of the line segment is:

D = √[(x_{2}−x_{1})^{2} + (y_{2}−y_{1})^{2}]. Here, (x_{1},y_{1}) and (x_{2}, y_{2}) are the coordinates of the endpoints.

For example, calculate the distance if a line segment has the following coordinates: (-1, 1) and (4, –3). Let us apply the distance formula to find the length of the line segment. Here,

x_{1 }= -1; x_{2} = 4; y_{1} = 1; y_{2} = -3.

Substitute the values in the distance formula to have:

D =√[(4-(-1))^{2} + (-3-1)^{2}) = √((4+1)^{2 }+ (-3-1)^{2}] = √(5)^{2}+ (-4)^{2}) = √(25 + 16) = √41 = 6.40 units. Therefore, using the distance formula, we found that the length of the line segment with coordinates (-1, 1) and (4, –3) is 6.40 units.

### Practice Questions

Practice these questions and compare your answers to test your knowledge of line segments.

#### Question 1

A line segment is a:

- One-dimensional figure
- Two-dimensional figure
- Three-dimensional figure
- None of these

**Answer**: A. Line segments are one-dimensional figures. They have only length with no width.

#### Question 2

Which of these has two end-points?

- Line segment
- Ray segment

**Answer**: Line segment. A line segment has two endpoints.

#### Question 3

When the coordinates of the two endpoints are given, the length of a line segment can be calculated using the distance formula.

- True
- False

**Answer**: True. The length of a line segment can be determined if you have the coordinates of two endpoints.

#### Question 4

Identify if the given figure is a line segment, a line, or a ray.

M <--------------------------------------> N

**Answer**: MN is a line. The figure has two points with an arrow on both ends. This shows that it is not a line segment or a ray but a line.

#### Question 5

Find the length of the line segment PQ if the coordinates of P and Q are (2, 4) and (1, 0), respectively.

**Answer**: x_{1 }= 2; x_{2} = 1; y_{1} = 4; y_{2} = 0.

Substitute the values in the distance formula to have:

D =√[(3-1)^{2} + (0-4)^{2}) = √(2)^{2}+ (-4)^{2}) = √(4 + 16) = √20 = 4.47 units. Therefore, using the distance formula, we found that the length of the line segment with coordinates (2, 4) and (1, 0) is 4.47 units

#### Question 6

How Many line segments does a Pentagon have?

- Five
- Six
- Two
- Three

**Answer**: A pentagon has 5 line segments

#### Question 7

Which of these is the unit of line segment?

- Liters
- Centimeter
- Kilogram
- Cubic meter

**Answer**: Centimeter is a metric unit used to measure the line segment.