The distance between points (x1,y1) and (x2,y2) is given by:

The distance between points (x1,y1) and (x2,y2) is given by:

• A. d = |x2 - x1| + |y2 - y1|
• B. d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
• C. d = sqrt[(x2 - x1)^2 - (y2 - y1)^2]
• D. d = sqrt[(x2 - x1)^2 + (y2 + y1)^2]

Answer: (B)

The distance between two points is found by the straight-line length of the segment connecting them, which comes from the Pythagorean theorem. You look at how far apart they are horizontally and vertically: Δx = x2 − x1 and Δy = y2 − y1. The distance is the length of the hypotenuse, so d = sqrt(Δx^2 + Δy^2) = sqrt[(x2 − x1)^2 + (y2 − y1)^2]. This is the standard Euclidean distance in the plane and it’s always nonnegative and symmetric in the two points. The other forms don’t measure the same thing: summing the absolute differences gives a grid-based distance rather than straight-line distance; subtracting the squares or mixing coordinates with a plus in the vertical term does not reflect the actual horizontal and vertical differences needed to form the hypotenuse.

The distance between two points is found by the straight-line length of the segment connecting them, which comes from the Pythagorean theorem. You look at how far apart they are horizontally and vertically: Δx = x2 − x1 and Δy = y2 − y1. The distance is the length of the hypotenuse, so d = sqrt(Δx^2 + Δy^2) = sqrt[(x2 − x1)^2 + (y2 − y1)^2]. This is the standard Euclidean distance in the plane and it’s always nonnegative and symmetric in the two points.

The other forms don’t measure the same thing: summing the absolute differences gives a grid-based distance rather than straight-line distance; subtracting the squares or mixing coordinates with a plus in the vertical term does not reflect the actual horizontal and vertical differences needed to form the hypotenuse.