Distance formula
The distance formula gives the straight-line distance between two points on the coordinate plane.
Practice This ConceptMain explanation
Teacher explanation
It comes from the Pythagorean theorem applied to the horizontal and vertical changes between two points. First find the difference in x-coordinates and y-coordinates, then square both changes, add them, and take the square root. This method works for every pair of points, even when they lie in different quadrants.
Example
For points A(2, 5) and B(6, 8), the horizontal change is 4 and the vertical change is 3, so the distance is sqrt(4^2 + 3^2) = 5 units.
Simple analogy
Move sideways, move up or down, then use the root.
Common confusion
Students often add the coordinate differences directly instead of squaring them and taking the square root.
Exam tip
Write the coordinates in the correct order first, then use the formula carefully. The sign will not matter after squaring, but the coordinates must still be read correctly.
Answer writing and exam use
1-mark use
Write the exact meaning of distance formula in one clean line.
2-mark use
Define distance formula and add one example or condition.
3-mark use
Explain distance formula, show the method or example, and mention the common mistake.
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