- What is the midpoint formula?
- M = ((x₁ + x₂)/2, (y₁ + y₂)/2). Add the two x-values and halve them, then do the same with the two y-values. For (2, 3) and (6, 7), that's (2 + 6)/2 = 4 and (3 + 7)/2 = 5, so the midpoint is (4, 5). It's just the average of the x's and the average of the y's, which is why the midpoint always sits exactly on the segment, the same distance from both ends.
- How do I find a missing endpoint when I know the midpoint?
- Use B = (2xₘ − x₁, 2yₘ − y₁): double the midpoint and subtract the endpoint you know. With endpoint (1, 2) and midpoint (4, −1), you get 2(4) − 1 = 7 and 2(−1) − 2 = −4, so the other endpoint is (7, −4). Check it by running the midpoint formula forward: (1 + 7)/2 = 4 and (2 + (−4))/2 = −1. Switch the tool to Missing endpoint and it does this for you, steps included.
- Can I enter fractions and negative numbers?
- Yes. Type fractions as a/b, like 1/2 or -3/4, and negatives with a minus sign. The math runs on exact fractions, so nothing gets rounded along the way. For (1/2, −3/4) and (5/2, 1/4), the midpoint is (1.5, −0.25), and the tool also shows the exact form (3/2, −1/4), which is the version most algebra teachers want written down.
- Why does my answer have a ≈ sign in front of it?
- Because that decimal never ends, so it's been rounded to 6 places. The midpoint of (0, 0) and (1/3, 2/3) is exactly (1/6, 1/3), which is 0.1666… and 0.3333… forever. The tool shows (≈0.166667, ≈0.333333) and puts the exact fraction on the line below. If your answer key uses fractions, copy that line instead of the decimals.
- Why do some calculators show 0.15000000000000002?
- Most calculators store numbers in binary floating point, which can't hold 0.1 or 0.2 exactly, so tiny errors leak into the result. The midpoint of (0.1, 0.2) and (0.2, 0.4) should be (0.15, 0.3), but a float-based calculator can print 0.15000000000000002. This one reads every digit you type as an exact fraction, so you get (0.15, 0.3). It also stays exact for huge whole numbers past 9,007,199,254,740,991, where floats start skipping values.
- How far is the midpoint from each endpoint?
- Exactly half the length of the segment, on both sides. For (2, 3) and (6, 7), the whole segment is √((6 − 2)² + (7 − 3)²) = √32 ≈ 5.657 long, and the distance from (2, 3) to the midpoint (4, 5) is √8 ≈ 2.828, which is half. If you need the length itself, the Distance Formula Calculator works it out from the same two points.
- How do I find a point a third of the way along a segment instead of halfway?
- Use P = (x₁ + t(x₂ − x₁), y₁ + t(y₂ − y₁)), where t is the fraction of the way from the first point. For A = (0, 0) and B = (6, 9) with t = 1/3, you get (0 + 6/3, 0 + 9/3) = (2, 3). The midpoint is the special case t = 1/2. This tool only does the halfway point, but the formula is the same idea.
- How does the midpoint help find a perpendicular bisector?
- The perpendicular bisector passes through the midpoint, and its slope is the negative reciprocal of the segment's slope. For (2, 3) and (6, 7), the midpoint is (4, 5) and the slope is (7 − 3)/(6 − 2) = 1, so the bisector's slope is −1. Point-slope form gives y − 5 = −(x − 4), which simplifies to y = −x + 9. The Slope Calculator gives you the slope part.
- Does this work for 3D points?
- Not in this tool, which is 2D only. The formula carries over, though: average the z-values the same way you average x and y. The midpoint of (1, 2, 3) and (5, 6, 7) is ((1 + 5)/2, (2 + 6)/2, (3 + 7)/2) = (3, 4, 5).
- Is what I type saved or sent anywhere?
- No. The math runs in your browser. Nothing you type is sent to a server or stored, and closing the tab clears it.
