‘How many endpoints does a line segment have? How many midpoints does a line segment have?
The correct Answer and Explanation is:
A line segment has exactly two endpoints because it is a finite portion of a line, beginning at one point and ending at another. Unlike a line, which extends infinitely in both directions, a line segment is a measurable entity with fixed endpoints.
A line segment has only one midpoint because the midpoint is defined as the unique point that is equidistant from both endpoints. The midpoint divides the segment into two equal halves, making it the sole center of the segment.
Explanation:
A line segment is one of the fundamental concepts in geometry. It represents the shortest path between two points in a straight line. Unlike a ray, which extends infinitely in one direction from a given point, a segment is bounded by two distinct endpoints.
The endpoints serve as markers that define the limits of the segment. They are important in various geometrical constructions and calculations, such as finding the length of the segment using the distance formula.
The midpoint of a line segment is a significant point in geometry because it represents the center of the segment. The midpoint’s location can be determined using the midpoint formula:
M=(x1+x22,y1+y22)M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of the two endpoints. This formula calculates the arithmetic mean of the x-coordinates and y-coordinates, resulting in the exact middle of the segment.
The concept of a midpoint is widely applied in various fields, including architecture, physics, and computer graphics. It helps in symmetry, balancing structures, and creating evenly divided segments.
