Finding the Midpoint of a Segment (Grades 6–8)
The midpoint is the point exactly halfway between two points.
Understanding finding the midpoint
Find it by averaging the x-coordinates and averaging the y-coordinates: midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). The midpoint of (2, 4) and (6, 8) is ((2+6)/2, (4+8)/2) = (4, 6).
Seeing it in action
Worked example
Midpoint of (2, 4) and (6, 8)?
x: (2 + 6)/2 = 4. y: (4 + 8)/2 = 6. → (4, 6).
Average x-values and y-values separately.
A common mistake, and the fix
Taking half the difference instead of the average.
For (2, 4) and (6, 8), half of 6 − 2 is 2, but that is only how far the midpoint’s x-coordinate sits from each end’s x-coordinate, not where the midpoint is. Add before halving: (2 + 6) ÷ 2 = 4 and (4 + 8) ÷ 2 = 6, so the midpoint is (4, 6).
Try a few
Midpoint of (0, 0) and (4, 6)?
(0 + 4)/2 and (0 + 6)/2.
Midpoint of (1, 2) and (5, 2)?
(1 + 5)/2 and (2 + 2)/2.
Midpoint of (2, 2) and (8, 10)?
(2 + 8)/2 and (2 + 10)/2.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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