How is Euclidean Distance calculated?

Euclidean Distance is a measure of the straight-line distance between two points in Euclidean space, and it is calculated using the Pythagorean theorem. To find the Euclidean Distance between two points, you start by computing the differences in their coordinates. For two points ( (x_1, y_1) ) and ( (x_2, y_2) ), the formula is:

[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

]

In this context, if we let ( A ) and ( B ) represent the differences in the coordinates of two points, the process involves squaring both differences (thus “the square of A and B”), adding these squares together, and then taking the square root of that sum. This is consistent with the second choice, signifying that taking the square root after summing the squared differences precisely captures the concept behind calculating Euclidean Distance.

The other choices do not accurately represent the steps necessary to compute the distance between two points in a way that adheres to the syntax of the correct formula used in geometry.