What is the distance between points (x1, y1) and (x2, y2)?

• A. sqrt((x2 - x1)^2 - (y2 - y1)^2)
• B. sqrt((x2 - x1) + (y2 - y1))
• C. sqrt((x2 - x1)^2 + (y2 - y1)^2)
• D. sqrt((x2 - x1)^2 + (y2 - y1))

Answer: (C)

Distance between two points is found by applying the Pythagorean theorem. The horizontal difference Δx = x2 − x1 and the vertical difference Δy = y2 − y1 are the legs of a right triangle, and the straight-line distance is the hypotenuse. So the distance is d = sqrt[(Δx)^2 + (Δy)^2], which in coordinates is sqrt[(x2 − x1)^2 + (y2 − y1)^2]. This matches the form that squares both coordinate differences and adds them before taking the square root.

The other forms don’t follow this rule: subtracting the squared differences; taking the square root of a sum without squaring either difference; or omitting the square on the vertical difference all fail to give the actual distance.