Midpoint Formula
Overview
The midpoint of a segment is the point that splits it into two congruent segments, so it sits exactly halfway between the endpoints. On a number line the midpoint is the average of the two coordinates; on the coordinate plane, average the x-coordinates and the y-coordinates separately. Averaging also runs backward: given one endpoint and the midpoint, the other endpoint is the same distance past the midpoint.
Vocabulary
- Midpoint
- The point that divides a segment into two congruent segments. The midpoint is equidistant from both endpoints.
- Segment Bisector
- A point, line, ray, line segment, or plane that intersects a segment at its midpoint.
- Equidistant
- At the same distance. The midpoint of a segment is equidistant from the segment's endpoints.
- Midpoint Formula
- The midpoint of the segment joining A(x₁, y₁) and B(x₂, y₂) is M = ((x₁ + x₂)/2, (y₁ + y₂)/2): average the x-values and average the y-values.
Main Ideas
- Midpoint means average — add the two coordinates and divide by 2. On the plane, do this once for x and once for y.
- The midpoint is a point, so a coordinate-plane answer is an ordered pair, not a single number.
- Working backward: each coordinate of the unknown endpoint is twice the midpoint coordinate minus the known endpoint coordinate.
- Check by distance: the midpoint must be the same distance from both endpoints.
Lesson Notes
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Lesson Video
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Interactive Activity
Find midpoints on a number line and a coordinate plane, and work backwards from a midpoint to an endpoint.
Practice Problems
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