Finding Distance and Midpoint

Pre-Algebra · Axiom Academy

EXAMPLE Finding Distance and Midpoint Work out the distance between two points and the midpoint between them using coordinate-geometry formulas. Given the two points below, find the distance between them and the coordinates of their midpoint. Nice work! You found both the distance and the midpoint between two points. Here's what to carry forward: Distance formula: . Subtract the coordinates, square each difference, add them, then take the square root. Midpoint formula: . Average the x-coordinates and average the y-coordinates. Watch the signs: subtracting a negative becomes addition, so 4 - (-2) = 6 , and squaring kills the sign: (-4)^2 = 16 . Two valid forms: the distance here is the exact radical or the decimal approximation — use whichever the problem asks for. These two formulas are core tools of coordinate geometry — they show up whenever you need the length of a segment or the point exactly halfway between two locations.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.