Coordinate distance is the hypotenuse of a horizontal-and-vertical right triangle.
WHAT HAPPENS IF…Does moving B from (3,2) to (-3,2) change its distance from the origin?
Interactive exploration
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Connect the picture to the idead=(x2−x1)2+(y2−y1)2
Translate the first point to the origin. Translation preserves distances. The coordinate differences give perpendicular legs, so Pythagoras gives the squared distance. The positive square root is used because length is nonnegative.
A detail that matters
Coordinate differences can be negative; distances cannot.