Enter the coordinates (x₁, y₁) and (x₂, y₂) into the calculator to determine the midpoint of the line segment.
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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.
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.
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:
In a Cartesian coordinate system, each point has two coordinates. These are shown on x and y axis like in the given below diagram.
To find the central point, having 2 endpoints of a line segment is important. Here are the steps to calculate the midpoint.
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)
➥ 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
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.
Yes, in 3D space, the midpoint formula extends to:
x = x₁ + x₂ 2 , y = y₁ + y₂ 2 , z = z₁ + z₂ 2
Here's how to find it:
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