Coordinate Geometry and Distance Formula from "summary" of NCERT Class 10 Mathematics Solutions by JagranJosh
Coordinate Geometry is an essential branch of mathematics that deals with the study of geometry using the coordinate system. In this system, points are located on the plane using ordered pairs of numbers known as coordinates. These coordinates help determine the position of a point in a two-dimensional space. The Distance Formula is a crucial formula used in Coordinate Geometry to calculate the distance between two points on a plane. This formula is derived from the Pythagorean theorem and helps find the distance between any two points given their coordinates. The Distance Formula is represented as d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points and d represents the distance between them. By applying this formula, one can easily determine the length of the line segment connecting the two points on the plane. This formula is particularly useful in various real-life scenarios, such as in navigation, physics, and engineering, where distances between points need to be calculated accurately. To understand the concept of Coordinate Geometry and the Distance Formula better, let's consider an example. Suppose we have two points A(3, 4) and B(7, 8) on a plane. To find the distance between these two points, we can substitute the coordinates into the Distance Formula. By applying the formula, we get d = √((7 - 3)² + (8 - 4)²) = √(4² + 4²) = √(16 + 16) = √32 ≈ 5.66 units. Therefore, the distance between points A and B is approximately 5.66 units.- Coordinate Geometry and the Distance Formula play a crucial role in mathematics and various other fields. By understanding these concepts, one can easily determine the position of points on a plane and calculate distances between them accurately. Mastering Coordinate Geometry and the Distance Formula is essential for solving a wide range of problems in mathematics and other disciplines.
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