The distance between two points in a coordinate system can be calculated using the distance formula, which is derived from the Pythagorean theorem. If you have two points, represented as (x1, y1) and (x2, y2), the distance (d) between these points is calculated as follows:
Distance Formula:
d = √((x2 – x1)2 + (y2 – y1)2)
To use this formula, follow these steps:
- Identify the coordinates of the two points. For example, let’s say Point A is (3, 4) and Point B is (7, 1).
- Substitute the coordinates into the formula:
- Calculate the differences:
7 – 3 = 4
1 – 4 = -3 - Square the differences:
(4)2 = 16
(-3)2 = 9 - Add these squares together:
16 + 9 = 25 - Finally, take the square root:
d = √25 = 5
d = √((7 – 3)2 + (1 – 4)2)
Therefore, the distance between Point A (3, 4) and Point B (7, 1) is 5 units.
This formula works for points on a two-dimensional plane, but it can also be extended to three dimensions or higher by including an additional coordinate (z, etc.). In general, the distance formula in three dimensions looks like this:
d = √((x2 – x1)2 + (y2 – y1)2 + (z2 – z1)2)
Understanding how to find the distance between two points can aid in various applications such as geometry, physics, computer graphics, and navigation. So whether you’re plotting a course, designing a game, or studying spatial relationships, mastering this technique is essential!