The midpoint formula gives the point halfway between (x1, y1) and (x2, y2): M = (x1 + x22, y1 + y22). You average the two x-coordinates and, separately, the two y-coordinates. For (2, 1) and (10, 7), the midpoint is (6, 4).
In Spanish
fórmula del punto medio
Also called
midpoint of a line segment formula, average of the endpoints
Look at the shadows on the axes: the midpoint’s x is halfway between the endpoints’ x-values, and its y is halfway between their y-values.
Formal definition and notation
The midpoint M of the segment with endpoints A(x1, y1) and B(x2, y2) is M(x1 + x22, y1 + y22). It lies on AB with AM = MB = 12AB, which can be checked with the distance formula. It is the special case of partitioning a segment in the ratio1 : 1.
Symbol
Read it as
Meaning
M
M
the usual name for a midpoint
AB
segment A B
the segment whose midpoint you want
Key facts
The midpoint is the average point: each coordinate is the mean of the endpoints’ coordinates.
Finding a missing endpoint: B = (2Mx − x1, 2My − y1). Double the midpoint and subtract the known endpoint.
The distance formula gives a length (a number) using squared differences. The midpoint formula gives a point (an ordered pair) using sums.
Quick check: 3 questions
Question 1 of 3
What is the midpoint of (0, 6) and (8, 0)?
Show answer and explanation
Answer: B.(0 + 82, 6 + 02) = (4, 3). (8, 6) adds without dividing, (−4, 3) subtracts the x-values, and (3, 4) swaps the coordinates.
Question 2 of 3
M(2, −1) is the midpoint of AB, and A = (−3, 4). What is B?
Show answer and explanation
Answer: C.B = (2 × 2 − (−3), 2 × (−1) − 4) = (7, −6). (−0.5, 1.5) averages A and M, (5, −5) is the change from A to M, and (−8, 9) goes the wrong way from A.
Question 3 of 3
Which point is the midpoint of the segment from (−5, −5) to (5, 5)?
Show answer and explanation
Answer: A.(−5 + 52, −5 + 52) = (0, 0), the origin. (10, 10) is the difference of the endpoints, and the others are endpoints or their reflections.
Midpoint Formula: frequently asked questions
Why does the midpoint formula average the coordinates?
Halfway along a segment means halfway in each direction. Horizontally, the point halfway between x1 and x2 on a number line is their average, x1 + x22. Vertically, the same holds for y. Putting the two averages together gives a point that splits the segment into two equal halves.
How do you find an endpoint from the midpoint?
Double the midpoint and subtract the endpoint you know, one coordinate at a time. If M = (4, 1) and one endpoint is (1, −3), the other is (2 × 4 − 1, 2 × 1 − (−3)) = (7, 5). Check: the average of (1, −3) and (7, 5) is (4, 1), as required.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS HSG-GPE.B.6, CCSS HSG-GPE.B.4
Cite this entry
Effortless Math Team. “Midpoint Formula.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/midpoint-formula/
Flashcard
TermMidpoint Formulaaverage the endpoints
DefinitionM = (x1 + x22, y1 + y22). Midpoint of (1, 3) and (7, 9) is (4, 6).
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