Distance Formula in Coordinate Geometry

What is distance formula in maths?

The distance formula in maths is used to find the distance between two points. If we have to find the distance between two points A (x₁, y₁) and B (x₂, y₂) then the formula is:

AB = √[(x₂−x₁)²+(y₂−y₁)²]

How is Pythagorean Theorem related to the distance formula?

The distance between two points (x₁,y₁) and (x₂,y₂) is calculated by:

Distance² = (x₂−x₁)²+(y₂−y₁)²

Distance = √[(x₂−x₁)²+(y₂−y₁)²]

What is Manhattan distance formula? 

Manhattan Distance is the distance measured between two points along the right angular axis. Manhattan Distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

D = |x₂ – x₁| +  |y₂ – y₁|

What is coordinate of a point?

Ordered pair (x,y) which is used to know the position of any point in the Cartesian plane is called the coordinate point. For example, (1,3) is a coordinate point.

What is distance formula in coordinate geometry?

The distance formula gives the shortest distance between two points in the coordinate geometry. The formula between the two points is given by:

d = √[(x₂−x₁)²+(y₂−y₁)²]

What is the formula for distance from origin?

The distance of any point P (x₁, y₁) from the origin O (0,0) is calculated using the formula:

OP = √[(x₁)² + (x₂)²]

What are different distance formulas in maths?

There are a number of distance formulas in maths including distance between two points, distance formula between point and a line, distance formula between two points etc.

How to calculate distance between two points?

To calculate the distance between two points in a two-dimensional Cartesian coordinate system, you use the distance formula: d = √[(x₂−x₁)²+(y₂−y₁)²]. In this formula, (x1, y1) and (x2, y2) represent the coordinates of the two points. You subtract the x-coordinates of the points, square the result, then subtract the y-coordinates and square the result. Add these squared values together, and finally, take the square root of the sum.

How to find distance between two points on a graph?

To find the distance between two points on a graph, you first locate the coordinates of the two points on the graph. Then, you can use the distance formula mentioned above to calculate the distance between them. This involves subtracting the x-coordinates of the points, squaring the result, subtracting the y-coordinates and squaring the result, adding these squared values together, and finally, taking the square root of the sum.

What is the shortest distance between two points?

In Euclidean geometry, the shortest distance between two points is a straight line. This is known as the Euclidean distance or the straight-line distance. It is the distance that would be traveled along a straight line between the two points, without any deviations or changes in direction. The distance formula mentioned above calculates the Euclidean distance between two points in a two-dimensional Cartesian coordinate system.

Distance Formula in Coordinate Geometry is used to compute the distance between two points, a point, and a line, and two line segments. The distance formula is based on the Pythagorean theorem. In the formula, d represents the distance, y2 is the y-coordinate of the second point, y1 is the y-coordinate of the first point, x2 is the x-coordinate of the second point, and x1 is the x-coordinate of the first point.

Coordinate geometry, commonly referred to as analytic geometry or Cartesian geometry, is a branch of geometry based on a coordinate system. Its applications include physics, engineering, air travel, rocketry, space research, and spaceflight.

In this article, we will learn about the distance between two points in coordinate geometry, the formula for the distance between two points, a point, a line, a point and a plane, and others in detail.