Coordinate geometry
Distance between the points
Pythagoras applied to the horizontal and vertical differences.
The Formula
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Pythagoras applied to the horizontal and vertical differences.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| d | Distance | units | The length of the segment joining the two points. |
| x2 - x1 | Horizontal change | units | The run between the two points. |
| y2 - y1 | Vertical change | units | The rise between the two points. |
What Each Symbol Means
dunits
Distance
The length of the segment joining the two points.
x2 - x1units
Horizontal change
The run between the two points.
y2 - y1units
Vertical change
The rise between the two points.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a midpoint page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Midpoint, filed under Math. Every number the guide produces comes from substituting into this one line.