Midpoint of a Line Segment Calculator

Enter the coordinates of the endpoints to get the midpoint, the step-by-step solution, and the graph of the line segment.

Point A

( , )

Point B

( , )

Result

The midpoint of the line segment whose endpoints are and is:

Quick Examples

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Solved Exercises

Calculate the midpoint of the segment with endpoints at (2, 4) and (6, 8).

Result

The midpoint of the segment whose endpoints are $ A(2, 4) $ and $ B(6, 8) $ is:

$$ M\left(4, 6\right) $$

Step-by-step solution

The formula for the midpoint M of a segment defined by the points A(x₁, y₁) and B(x₂, y₂) is:

$$ M = \left( \dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2} \right) $$

1. Identify the coordinates:

$$ \begin{aligned} x_1 &= 2, & y_1 &= 4 \\[1em] x_2 &= 6, & y_2 &= 8 \end{aligned} $$

2. Substitute the coordinates into the formula:

$$ M = \left( \dfrac{2 + 6}{2}, \dfrac{4 + 8}{2} \right) $$

3. Calculate the operations in the numerators:

$$ M = \left( \dfrac{8}{2}, \dfrac{12}{2} \right) $$

4. Final result:

$$ M\left(4, 6\right) $$

Graph of a segment and its midpoint on the Cartesian plane, example 1. — Graph of the segment and its midpoint

Determine the midpoint between A(-4, 2) and B(2, -6).

Solution

The midpoint of the segment whose endpoints are $ A(-4, 2) $ and $ B(2, -6) $ is:

$$ M\left(-1, -2\right) $$

Step-by-step solution

The formula for the midpoint M of a segment defined by the points A(x₁, y₁) and B(x₂, y₂) is:

$$ M = \left( \dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2} \right) $$

1. Identify the coordinates:

$$ \begin{aligned} x_1 &= -4, & y_1 &= 2 \\[1em] x_2 &= 2, & y_2 &= -6 \end{aligned} $$

2. Substitute the coordinates into the formula:

$$ M = \left( \dfrac{-4 + 2}{2}, \dfrac{2 + \left(-6\right)}{2} \right) $$

3. Calculate the operations in the numerators:

$$ M = \left( \dfrac{-2}{2}, \dfrac{-4}{2} \right) $$

4. Final result:

$$ M\left(-1, -2\right) $$

Graph of a segment and its midpoint on the Cartesian plane, example 2.

Find the midpoint of the segment whose endpoints are (1, 1/3) and (2, 2/3).

Answer

The midpoint of the segment whose endpoints are $ A(1, 1/3) $ and $ B(2, 2/3) $ is:

$$ M\left(\dfrac{3}{2}, \dfrac{1}{2}\right) = M(1.5, 0.5) $$

Step-by-step solution

The formula for the midpoint M of a segment defined by the points A(x₁, y₁) and B(x₂, y₂) is:

$$ M = \left( \dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2} \right) $$

1. Identify the coordinates:

$$ \begin{aligned} x_1 &= 1, & y_1 &= \dfrac{1}{3} \\[1em] x_2 &= 2, & y_2 &= \dfrac{2}{3} \end{aligned} $$

2. Substitute the coordinates into the formula:

$$ M = \left( \dfrac{1 + 2}{2}, \dfrac{\dfrac{1}{3} + \dfrac{2}{3}}{2} \right) $$

3. Calculate the operations in the numerators:

$$ M = \left( \dfrac{3}{2}, \dfrac{1}{2} \right) $$

4. Final result:

$$ M\left(\dfrac{3}{2}, \dfrac{1}{2}\right) = M(1.5, 0.5) $$

Graph of a segment and its midpoint on the Cartesian plane, example 3.

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Daniel Machado

Professor of Mathematics, graduated from the Faculty of Exact, Chemical and Natural Sciences of the National University of Misiones (UNAM). Developer and creator of RigelUp, dedicated to building tools for mathematical learning.