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Midpoint Calculator

Enter the coordinates (x₁, y₁) and (x₂, y₂) into the calculator to determine the midpoint of the line segment.

First Point Coordinates:

Second Point Coordinates:

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Midpoint Calculator

Use this midpoint calculator to find the midpoint between two given points in a cartesian coordinate system. Our tool provides step-by-step solutions and generates a graphical representation of the line segment to help you understand the process.

What is the Midpoint?

A midpoint is a point that lies exactly in the middle of a line segment, equidistant from both endpoints. It divides the segment into two equal parts.

Midpoint Formula:

The formula to find the coordinates of a midpoint on a cartesian plane is as follows. In this formula, the coordinates are represented by (x₁, y₁) and (x₂, y₂) and their midpoints by 'x' and 'y':

x = x₁ + x₂ 2

y = 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. 

midpoint of a line

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

x = x₁ + x₂ 2

x = 10 2

x = 5

Step # 3 = Add the y-coordinates

y₁ + y₂

= 5 + 1

= 6

Step # 4 = Divided by 2

y = y₁ + y₂ 2

y = 6 2

y = 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

FAQs:

What happens if the two endpoints are the same point?

If both endpoints are the same, the midpoint will also be the same as the endpoints, as the line segment collapses into a single point.

Can the midpoint formula be applied in three-dimensional space?

Yes, in 3D space, the midpoint formula extends to:

x = x₁ + x₂ 2 , y = y₁ + y₂ 2 , z = z₁ + z₂ 2

What is the midpoint of 10 and 20?

Here's how to find it:

  • Add the two numbers: 10 + 20 = 30
  • Divide the sum by 2: 30 / 2 = 15
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