Midpoint of a Line Segment
This interactive tool helps you find the midpoint of a line segment on a coordinate grid — the point exactly halfway between two endpoints. Explore it visually by dragging the points, then switch to a written, step-by-step calculation.
Using the Find menu you can also work backwards: given one endpoint and the midpoint, find the missing endpoint.
How to Use
Tab Navigation
Switch between the activities using the tabs:
- Midpoint: Drag the endpoints on the grid and reveal the coordinates of A, B and the midpoint.
- Calculate: See the question written out, then draw the worked solution with the pen.
- 🎨 Settings: Change the grid style and the segment colour.
Shared Controls
Three controls sit below both tabs:
- The Find menu chooses the task — Find the midpoint or Find an endpoint.
- New problem generates a fresh pair of points.
- Difficulty shapes those generated problems. 1 · Easy keeps both points in the positive quadrant and always lands the midpoint on a whole number. 2 · Medium stays positive, but the midpoint can be a half. 3 · Hard uses the whole grid, including negative coordinates. It only affects New problem — you can always drag the points anywhere, whatever the level.
📍 Midpoint
The Midpoint tab is for exploring on the grid.
🧭 How to Use the Tool
Drag endpoints A and B to change the segment. Click A = (?, ?) and B = (?, ?) to reveal each endpoint, and Midpoint = (?, ?) to check the point in the middle.
With Find set to Find an endpoint, one endpoint and the midpoint are shown while the other endpoint is hidden — work out where it must be, then reveal to check.
The midpoint is the average of the two coordinates:
Midpoint = ( (x₁ + x₂) ÷ 2 , (y₁ + y₂) ÷ 2 )
The answer can be a half value (like 2.5) — the midpoint does not have to land on a grid corner.
✏️ Calculate
The Calculate tab writes the working by hand, using the current points.
🧭 How to Use the Tool
The question appears first — for example “Find the midpoint of AB, if A(6, −2) and B(−5, −3)”. Work it out yourself, then click Next step to reveal the working one line at a time — or Show all for the whole solution: the x-coordinates are added and halved, the y-coordinates are added and halved, giving the midpoint M.
Press New problem for another question, or use the Find menu to switch to the missing-endpoint calculation (B = 2M − A).