Midpoint Calculator

How to Calculate the Midpoint of a Line Segment

The midpoint of a line segment is the point that divides the segment into two equal parts. It's a fundamental concept in geometry and has various applications in mathematics and real-world scenarios.

Midpoint Formula

The midpoint formula is used to find the coordinates of the midpoint of a line segment given the coordinates of its endpoints. The formula is:

\[ \text{Midpoint} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]

Where:

• (x₁, y₁) are the coordinates of one endpoint
• (x₂, y₂) are the coordinates of the other endpoint

Calculation Steps

1. Identify the coordinates of the two endpoints: (x₁, y₁) and (x₂, y₂)
2. Calculate the x-coordinate of the midpoint: \[ x_m = \frac{x_1 + x_2}{2} \]
3. Calculate the y-coordinate of the midpoint: \[ y_m = \frac{y_1 + y_2}{2} \]
4. The midpoint is (x_m, y_m)

Example Calculation

Let's find the midpoint of a line segment with endpoints (2, 3) and (8, 9).

1. Identify the coordinates:
   • (x₁, y₁) = (2, 3)
   • (x₂, y₂) = (8, 9)
2. Calculate the x-coordinate of the midpoint: \[ x_m = \frac{x_1 + x_2}{2} = \frac{2 + 8}{2} = \frac{10}{2} = 5 \]
3. Calculate the y-coordinate of the midpoint: \[ y_m = \frac{y_1 + y_2}{2} = \frac{3 + 9}{2} = \frac{12}{2} = 6 \]
4. The midpoint is (5, 6)

Visual Representation

A visual representation can help understand the concept better. Here's a diagram showing the line segment with endpoints (2, 3) and (8, 9), and its midpoint (5, 6):

This diagram illustrates how the midpoint (5, 6) divides the line segment into two equal parts.