Midpoint of a line segment
Definition: A point on a line segment that divides it into two equal parts
The halfway point of a line segment
Try this
Adjust the line segment below by dragging an orange dot on an endpoint and see how the point M
always divides the segment PQ into two equal halves.
See the figure above. The point M is the midpoint of the
line segment PQ.
Only a line segment can have a midpoint. A
line
cannot since it goes on indefinitely in both directions, and so has no midpoint.
A ray
cannot because it has only one end, and hence no midpoint.
When a line cuts another line into two equal parts it is called a
bisector.
The bisector will cut the line at its midpoint. The midpoint of a line segment can be found using a compass and straightedge.
See Constructing the perpendicular bisector of a line segment.
Riemann sums that use the left or right endpoints on the intervals can be used to find the height of the rectangles. On this page we explore the midpoint method uses a point in the middle of the interval to find the height of the rectangle, and the trapezoid method that uses a trapezoid instead of a rectangle to approximate the area of each interval. Interactive calculus applet.
This construction shows how to draw the perpendicular bisector of a given line segment with compass and straightedge or ruler. This both bisects the segment (divides it into two equal parts), and is perpendicular to it. Finds the midpoint of a line segmrnt. The proof shown below shows that it works by creating 4 congruent triangles. A Euclideamn construction.
Finding the midpoint of a line segment given the coordinates of the endpoints
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