To find the length of a line segment, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is typically used to calculate the distance between two points in a coordinate plane.
Suppose you have two points, A and B, with coordinates A(x1, y1) and B(x2, y2). The length of the line segment AB can be found using the formula:
D = √((x2 - x1)2 + (y2 - y1)2)
Here’s a step-by-step explanation:
- Identify the coordinates: Determine the coordinates of the two endpoints of the line segment.
- Subtract the x-coordinates: Calculate the difference between the x-coordinates of the two points (x2 – x1).
- Subtract the y-coordinates: Calculate the difference between the y-coordinates of the two points (y2 – y1).
- Square the differences: Square both differences you calculated in the previous two steps.
- Add the squares: Add the squared differences together.
- Take the square root: Finally, take the square root of the sum to find the length of the line segment.
For example, if point A is (2, 3) and point B is (5, 7), the length of line segment AB would be calculated as:
D = √((5 - 2)2 + (7 - 3)2) = √(32 + 42) = √(9 + 16) = √25 = 5
So, the length of the line segment AB is 5 units.