Distance Between Two Points
There is a right triangle hiding between any two points: one leg across, one leg up, and the line joining them as the long side. Move the points and it draws itself.
Distance √65 ≈ 8.06
- Across
- 7
- Up
- 4
Try one
Drag either point, or tab to one and use the arrow keys.
Ready to try some? Distance between two points worksheets
Where it usually goes wrong
The distance between two points gets found by adding the across and the up, which is how far you would walk around two sides of a block rather than how far apart the corners are. The other half is subtracting the coordinates the wrong way around and worrying about the minus sign — squaring settles that, and distance is never negative.
Try this
- Press A 3-4-5 and read the legs. Three across, four up, and the answer is five rather than seven.
- Drag a point so the two are on opposite sides of an axis. The legs are still positive lengths.
- Press Not a whole number. Most pairs of points are like this one; the tidy ones are the exception.
Where this goes next
This is Pythagoras with the squares taken off the sides, and it is how distance is computed on every map and in every piece of graphics software.
More about graphs and data
- The Discriminantthe sign of b² − 4ac is the sign of the parabola's own height above or below the x-axis
- Horizontal and Vertical Function Shiftsa horizontal shift's sign points the opposite way from the move
- Systems of Linear Equationsa system of two lines has one solution where they cross, none if they run parallel, or infinitely many if they are the same line twice