Math Resources Hub

Midpoint

The midpoint is the point exactly halfway between two others. Finding it is one of the friendliest moves in coordinate geometry: just average the xx-coordinates and average the yy-coordinates. It's the foundation for perpendicular bisectors, centers of figures, and symmetry — and it builds right on the coordinate plane.

Skill

Midpoint

  1. What & why

    Halfway between two numbers is their average — halfway between 22 and 88 is 2+82=5\frac{2 + 8}{2} = 5. The midpoint of a segment just does this in both directions at once:

    M=(x1+x22, y1+y22)M = \left(\frac{x_1 + x_2}{2}, \ \frac{y_1 + y_2}{2}\right)

    Average the xx's for the midpoint's xx, average the yy's for its yy. The one trap is adding without halving — the sum of the endpoints overshoots the middle by double.

  2. Watch how it works

    Take the segment from (2,2)(2, 2) to (8,6)(8, 6). Average each coordinate:

    M=(2+82, 2+62)=(5,4)M = \left(\frac{2 + 8}{2}, \ \frac{2 + 6}{2}\right) = (5, 4)

    The midpoint (5,4)(5, 4) lands squarely in the center of the segment:

    ABM
    M (5, 4) is the average of A (2, 2) and B (8, 6) — dead center.

    Watch the signs when a coordinate is negative: the midpoint of (−4,1)(-4, 1) and (6,9)(6, 9) has x=−4+62=1x = \frac{-4 + 6}{2} = 1.

  3. Reason through one together

    Average the xx's and the yy's separately — don't forget to halve. Predict before you check.

    Make a prediction: What is the midpoint of (2, 2) and (8, 6)?

  4. Practice until it’s automatic

    Fresh problems, one at a time. Build a streak — the goal is getting them right without stopping to think.

    Streak0/ 5Accuracy0%(0/0)

    What is the y-coordinate of the midpoint of (-6, -3) and (2, 5)?

  5. Prove it

    Harder, applied problems at the level you’ll meet on the Regents. Get them all right to earn this skill.

    Question 1 of 8

    What is the x-coordinate of the midpoint of (2, 4) and (8, 10)?

For teachers

Standard, common misconceptions, and suggested use will live here.