Read the result
Read the diagram as two movements: across and up, then directly from A to B. The direct segment is the distance; the dashed legs explain why Pythagoras appears.
Coordinate geometry
Distance Between Two Points
Measure the shortest route between two coordinates, with the right-triangle behind the formula drawn beside the answer.
Formula
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Result
Worked substitution
The horizontal and vertical coordinate changes form the two short sides of a right triangle.
Where it helps
Useful when a geometry problem gives endpoints but asks for a length, radius, displacement, or spacing between two positions.
Common slip
Do not subtract coordinates in different orders for x and y. The squares hide the sign in the final distance, but the working becomes harder to check.
Try it
Try A(-3, 4) and B(5, -2). Before looking at the answer, estimate whether the distance should be nearer 8, 10, or 12.