In Exercises 105–106, find the midpoint of each line segment with the given endpoints. (2, 6) and (-12, 4)

Key Concepts

Midpoint Formula

The midpoint formula is used to find the point that is exactly halfway between two given points in a coordinate plane. It is calculated using the formula M = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints. This concept is essential for determining the midpoint of a line segment.

Coordinate Plane

A coordinate plane is a two-dimensional surface formed by the intersection of a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on this plane is represented by an ordered pair (x, y), which indicates its position relative to the axes. Understanding the coordinate plane is crucial for visualizing and solving problems involving points and line segments.

Distance Between Points

The distance between two points in a coordinate plane can be calculated using the distance formula, which is derived from the Pythagorean theorem. The formula is D = √((x2 - x1)² + (y2 - y1)²). While not directly needed for finding the midpoint, understanding this concept helps in grasping the relationship between points and their positions on the plane.