Distance Between Two Points
How do I calculate the distance between two points?
- The distance between two points with coordinates and can be found using the formula
- This formula is really just Pythagoras’ Theorem , applied to the difference in the -coordinates and the difference in the -coordinates;
- You may be asked to find the length of a diagonal in 3D space. This can be answered using 3D Pythagoras
Exam Tip
- As we are squaring the difference in and in the formula, it does not matter if they are positive or negative
- 32 is the same as (-3)2, this may help to speed up your working
Worked example
Point A has coordinates (3, -4) and point B has coordinates (-5, 2).
Calculate the distance of the line segment AB.
Using the formula for the distance between two points,
Substituting in the two given coordinates:
Simplify:
Answer = 10 units