Midpoint Calculator

Midpoint Calculator

Calculate the midpoint between two cartesian coordinates by using this midpoint calculator in a complete step-by-step solution. The midpoint is the point that is located at the center of two points. 

Midpoint Formula:

The formula to find the coordinates of a midpoint on a cartesian plane is as follows:

M = x₁ + x₂ 2 , y₁ + y₂ 2

Where:

• x₁, x₂ = x-coordinates of the first point 
• y₁, y₂ = y-coordinates of second point

In a Cartesian coordinate system, each point has two coordinates. These are shown on x and y axis like in the given below diagram. 

How to Calculate the Midpoint?

To find the central point, having 2 endpoints of a line segment is important. Here are the steps to calculate the midpoint. 

• Sum the x-coordinates: Add x₁ and x₂
• Divide by 2: Divide the answer of 1st step by 2 to get x-coordinates of the midpoint 
• Sum the y-coordinates: Add y₁ and y₂
• Divide by 2: Divide the answer of step 3 by 2 to know y-coordinate of midpoint
• Combine coordinates:The midpoint is represented by the ordered pair (x, y), where x is the result from step 2 and y is the result from step 4

Example:

Suppose the coordinates of points as (2, 5) and (8, 1)

Step # 1 = Add the x-coordinates

x₁ + x₂ = 2 + 8 = 10

Step # 2 = Divided by 2

= x₁ + x₂ 2 = 10 2 = 5

Step # 3 = Add the y-coordinates

y₁ + y₂ = 5 + 1 = 6

Step # 4 = Divided by 2

= y₁ + y₂ 2 = 6 2 = 3

Step # 5 = Combine (x, y) coordinates

By combining the coordinates we get the midpoint between the given points as (5, 3)

Applications of Midpoint Calculator:

➥ Geometry: This tool helps to find the center of a line segments 

➥ Graphing: By using this calculator you can locate the midpoint of a lines

➥ Data analysis:Find the average position between two points 

➥ Mechanics: For simple systems, the tool calculates the center of a mass

➥ Kinematics: It calculates the average position of objects over time

➥ Optics:The calculator helps to determine the focal point of a lens or mirror