Midpoint Formula with Examples
The midpoint formula finds the point exactly halfway between (x₁, y₁) and (x₂, y₂): M = ((x₁ + x₂) ⁄ 2, (y₁ + y₂) ⁄ 2). You just average the x’s and average the y’s.
Distance & Midpoint
The distance between two points on a coordinate plane is the Pythagorean theorem applied to the horizontal and vertical gaps.
- Distance
- d = √((x2 − x1)2 + (y2 − y1)2)
- Midpoint
- M = ((x1 + x2) ⁄ 2, (y1 + y2) ⁄ 2)
- Slope
- m = (y2 − y1) ⁄ (x2 − x1)
- (x₁, y₁) first point
- (x₂, y₂) second point
Example 1
Find the midpoint of (2, 3) and (8, 11).
- x = (2 + 8) ÷ 2 = 5
- y = (3 + 11) ÷ 2 = 7
- M = (5, 7)
Example 2: with negatives
Find the midpoint of (−4, 6) and (2, −10).
- x = (−4 + 2) ÷ 2 = −1
- y = (6 + (−10)) ÷ 2 = −2
- M = (−1, −2)
Example 3: find a missing endpoint
M = (3, 5) is the midpoint of A(1, 2) and B. Find B.
- (1 + x) ÷ 2 = 3, so x = 5
- (2 + y) ÷ 2 = 5, so y = 8
- B = (5, 8)
Try the distance and midpoint calculator
Try it yourself
Find the midpoint of (0, 0) and (7, −3).
Show the answer
M = (3.5, −1.5)
The distance and slope formulas are on the distance and midpoint formulas page. See also our distance formula guide.
Midpoint formula: FAQ
What is the midpoint formula?
M = ((x₁ + x₂) ⁄ 2, (y₁ + y₂) ⁄ 2).
How do I find an endpoint from the midpoint?
Double the midpoint and subtract the known endpoint: x₂ = 2Mx − x₁ and y₂ = 2My − y₁.
Can the midpoint have decimals?
Yes. If the sum is odd, the midpoint is a half, such as 3.5.