Midpoint Formula in Geometry

The midpoint formula finds the point exactly halfway between two points (x₁, y₁) and (x₂, y₂). It is $M = \left(\dfrac{x_1 + x_2}{2},\ \dfrac{y_1 + y_2}{2}\right)$ . In words: average the two x-coordinates to get the midpoint’s x, and average the two y-coordinates to get its y. The midpoint always lies on the segment joining the points, splitting it into two equal halves.

Interactive midpoint explorer

Drag point A or B (or click a point and use the arrow keys). The midpoint M is marked in amber and its coordinates update live.

Drag a point, or click it and use the arrow keys. Coordinates snap to the grid.

Point A (x₁, y₁)

Point B (x₂, y₂)

Midpoint (1, 1)

Step-by-step substitution

M = ((x₁+x₂)/2, (y₁+y₂)/2) = ((-4+6)/2, (-2+4)/2) = (1, 1)

Why it works

The midpoint is the average position of the two endpoints. Averaging the x-coordinates gives a point horizontally centered between them; averaging the y-coordinates centers it vertically. The result is the unique point equidistant from both ends along the segment.

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

Worked examples

(2, 3) and (8, 7): M = ((2+8)/2, (3+7)/2) = (10/2, 10/2) = (5, 5).
(0, 0) and (3, 4): M = ((0+3)/2, (0+4)/2) = (1.5, 2).
(−4, −2) and (6, 4): M = ((−4+6)/2, (−2+4)/2) = (2/2, 2/2) = (1, 1).

Practice problems

(0, 0) and (10, 6)
Answer
(5, 3)
(1, 1) and (7, 9)
Answer
(4, 5)
(−6, 2) and (2, −4)
Answer
(−2, −1)
(3, 5) and (4, 8)
Answer
(3.5, 6.5)
(−5, −5) and (5, 5)
Answer
(0, 0)

Classroom use: midpoint formula formulas

Who it's for: Grades 6–12 · Students finding segment midpoints on the coordinate plane, and high-school students partitioning directed segments.

Learning objectives

After using this page, students will be able to:

Compute a midpoint by averaging the x- and y-coordinates.
Find an endpoint given the midpoint and the other endpoint.
Use midpoints to locate the centre of a circle or the diagonals of a parallelogram.

Suggested classroom activity

Emphasise that the midpoint is an average, not a difference — the confusion with the distance formula is the recurring error. Have students drag one endpoint and watch the midpoint move at half the rate; that halved motion is the formula made visible.

Standards alignment

Aligned to the Common Core State Standards for Mathematics. Codes are given exactly as published so they can be matched against state crosswalks.
Code	Standard
`HSG.GPE.B.6`	Find the point on a directed line segment that partitions it in a given ratio.
`6.G.A.3`	Draw polygons in the coordinate plane; use coordinates to find side lengths.

Free to use and adapt in class under the terms on our license page — no account, no sign-up, no ads. Content last reviewed August 2026.

Frequently asked questions

What is the midpoint formula in geometry?

The midpoint formula finds the point exactly halfway between (x₁, y₁) and (x₂, y₂): M = ((x₁ + x₂)/2, (y₁ + y₂)/2). It is simply the average of the x-coordinates and the average of the y-coordinates.

How do you find the midpoint of a line segment?

Average the endpoints’ coordinates: add the two x-values and divide by 2, then add the two y-values and divide by 2. For (2, 3) and (8, 7), the midpoint is (5, 5).

Can the midpoint have decimal coordinates?

Yes. If the sum of two coordinates is odd, the midpoint coordinate is a half. For (0, 0) and (3, 4), the midpoint is (1.5, 2). That is perfectly valid.