Skill: Determine the midpoint of a line segment

Explanation and Free Practice Resources

The midpoint of a line segment in the Cartesian plane is the point halfway between its endpoints, with equal distance to each endpoint; its coordinates are found by averaging the corresponding $x$ -coordinates and the corresponding $y$ -coordinates, $M\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$ , including results that may be fractions or decimals. This understanding supports coordinate proofs, distance relationships, and geometric transformations; the scope is limited to two-dimensional Cartesian coordinates, not three-dimensional or more abstract vector generalizations.

On this page:

Learn “Determine the midpoint of a line segment” with a detailed explanation of the concept
Master “Determine the midpoint of a line segment” with unlimited, free practice problems
Download (or modify) a free worksheet on Determine the midpoint of a line segment you can use at home or in class with practice problems that scaffold and explore “Determine the midpoint of a line segment” from different perspectives.
Start working on adaptive units like “Line Equations and Graphing - Practice” or “Segments, Mid-Points, and Perpendicular Bisectors - Intro” that introduce, teach, or practice “Determine the midpoint of a line segment” to maximize your learning.

Detailed Explanation: Determine the midpoint of a line segment

The midpoint is the point exactly halfway between the two endpoints of a line segment. To find it, average the two $x$ -coordinates and average the two $y$ -coordinates:

M\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)

Example

Find the midpoint of the segment with endpoints $A(-3,5)$ and $B(7,-1)$ .

Step 1: Identify the coordinates.

x_1=-3,\quad y_1=5,\quad x_2=7,\quad y_2=-1

Step 2: Average the $x$ -coordinates.

\frac{x_1+x_2}{2} =\frac{-3+7}{2} =\frac{4}{2} =2

Step 3: Average the $y$ -coordinates.

\frac{y_1+y_2}{2} =\frac{5+(-1)}{2} =\frac{4}{2} =2

Step 4: Write the midpoint.

\boxed{M(2,2)}

So, the midpoint of the segment from $(-3,5)$ to $(7,-1)$ is $(2,2)$ . Always average corresponding coordinates: the $x$ -coordinates together and the $y$ -coordinates together.

Learn by doing: Determine the midpoint of a line segment

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Your results

Practice with unlimited practice problems

Line Segment (Points) - Find Midpoint (Coordinate)

Earned ?

Download/Modify Free Grade 11 'Determine the midpoint of a line segment' Worksheet

Print this free 'Determine the midpoint of a line segment' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.

Units Teaching This Skill

These adaptive units introduce, teach, or reinforce this skill (Determine the midpoint of a line segment) through scaffolded problems that grow in difficulty as concepts are understood.