What is the distance formula used for?

The distance formula is primarily used to calculate the length of a line segment between two points in a coordinate plane. It is derived from the Pythagorean theorem and provides a way to quantify the space between two points, represented as (x1, y1) and (x2, y2). The formula is expressed as:

[ \text{Distance} = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} ]

This calculation is crucial in various mathematical applications and scenarios, such as geometry and physics, where understanding the physical distance between points is necessary.

The other options pertain to different concepts in geometry. Finding the slope of a line involves determining the ratio of the vertical change to the horizontal change between two points, while determining the midpoint requires averaging the coordinates of two points rather than calculating the distance. Calculating the area of a triangle involves different formulas based on the dimensions of the triangle rather than the measurement of length between points.