Coordinate geometry: Distance between points In coordinate geometry, we use coordinates (x, y) to locate points in a 2D plane. The distance between two poin...
Coordinate geometry: Distance between points
In coordinate geometry, we use coordinates (x, y) to locate points in a 2D plane. The distance between two points is a measure of how far apart they are.
Formula:
The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula:
d = √(x2 - x1)^2 + (y2 - y1)^2)
where d is the distance, x1 and y1 are the coordinates of the first point, and x2 and y2 are the coordinates of the second point.
Example:
Suppose you have two points:
A(3, 4)
B(7, 2)
Using the formula, we can calculate the distance between A and B:
d = √(7 - 3)^2 + (2 - 4)^2 = √4 + 16 = √20
Therefore, the distance between A and B is √20 units.
Applications:
The distance between points has numerous applications in various fields, including:
Geography: Calculating the distance between cities and towns.
Navigation: Determining the shortest route between two points on a map.
Science: Studying the distance between chemical elements or species.
Engineering: Designing structures and machines that can withstand or operate at a certain distance from a particular point