To find the length of a line segment in a two-dimensional space, you can use the distance formula derived from the Pythagorean theorem. The formula is as follows:
Distance = √((x2 – x1)² + (y2 – y1)²)
Here’s a step-by-step guide on how to calculate the length of a line segment:
- Identify the Endpoints: Determine the coordinates of the endpoints of the line segment. For instance, let’s say you have two points: Point A (x1, y1) and Point B (x2, y2).
- Substitute the Coordinates: Plug the coordinates of the points into the distance formula. For example, if Point A is (2, 3) and Point B is (5, 7), substitute those values into the formula:
- Calculate the Differences: Perform the subtraction:
- Square the Differences: Square the results:
- Add the Squares: Add the squared numbers:
- Find the Square Root: Finally, take the square root:
Distance = √((5 - 2)² + (7 - 3)²)
Distance = √((3)² + (4)²)
Distance = √(9 + 16)
Distance = √(25)
Distance = 5
So, the length of the line segment between Point A (2, 3) and Point B (5, 7) is 5 units.
In summary, by using these simple steps and the distance formula, you can easily determine the length of any line segment in a Cartesian plane. This method can also be extended to three-dimensional space with slight modifications, where you would add the z-coordinates into the equation as well.