A line segment can be defined as a straight geometric shape. Two ends describe a Line Segment. If ends of a Line Segment are written as coordinate then a Cartesian representation of a segment can be given. A line segment, like other geometric shapes has Point of Symmetry. This point is called as mid - point. Now question arises, how many midpoints does a segment have? Answer to this question is 1. A line segment can have only one mid – point. A mid – point divides the line segment into two halves. To find coordinates of this point, coordinates of ends of line segments must be known to us. This can further assist you in finding the length of line segment.
Suppose we have a line segment defined by two end points 'A' and 'B', such that their coordinates are: (3, 2) and (5, 4). General formulae we use to calculate the mid – point and length of line segment can be given as follows: Suppose coordinates of mid – point are given as (X, Y)
X = (XA + XB)/ 2 and Y = (YA + YB)/ 2,
Length = √((YB - YA)2 + (XB - XA) 2),
In given example we have, XA = 3, YA = 2, XB = 5, YB = 4. Substituting values of XA, YA, XB and YB in above two equations to calculate mid – point and length as:
X = (3 + 5)/ 2 = 4 and Y = (4 + 2)/ 2 = 3,
Length = √((4 - 2)2+ (5 - 3)2) = √ (4 + 4) = 2 √ (2) units.
So, coordinates of midpoint of line segment of length 2 √(2) units is: (4, 3).