Midpoint
A midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of the line, and the midpoint is between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.
In the coordinate plane if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points is ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4). Let us learn more about the formula of the midpoint, and different methods to find the midpoint of a line.
1.  What is Midpoint? 
2.  General Formula of Midpoint 
3.  Formulas Related to Midpoint 
4.  FAQs 
What is Midpoint?
A midpoint is a point lying between two points and is the middle of the line joining the two points. For the two points, if a line is drawn joining the two points, then the midpoint is a point at the middle of the line and is equidistant from the two points. Given any two points, say A and C, the midpoint is a point B which is located halfway between points A and C.
Observe that point B is equidistant from A and C. A midpoint exists only for a line segment. Aline or a ray cannot have a midpoint because a line is indefinite in both directions and a ray has only one end and thus can be extended.
General Formula of Midpoint
The midpoint formula is defined for the points in the coordinate axes. Let (x_{1}, y_{1}) and (x_{2}, y_{2}) be the endpoints of a line segment. The midpoint is equal to half of the sum of the xcoordinates of the two points, and half of the sum of the ycoordinates of the two points. The midpoint formula to calculate the midpoint of a line segment joining these points is:
Let us look at this example and find the midpoint of two points in one dimensional axis. Suppose, we have two points, 5 and 9, on a number line. The midpoint will be calculated as: ( 5 + 9)/2 = 14/2 = 7. So, 7 is the midpoint of 5 and 9.
Further based on the points and their coordinate values, the following two methods are used to find the midpoint of the line joining the two points.
Method 1: If the line segment is vertical or horizontal, then dividing the length by 2 and counting that value from any of the endpoints will get us the midpoint of the line segment. Look at the figure shown below. The coordinates of points A and B are (3, 2) and (1, 2) respectively. The length \(\overline{AB}\) is 4 units. Half of this length is 2 units. Moving 2 units from the point (3, 2) will give (1, 2). So, (1, 2) is the midpoint of \(\overline{AB}\).
Method 2: The other way to find the midpoint is by using the midpoint formula. The coordinates of points A and B are (3, 3) and (1, 4) respectively. Using midpoint formula, we have: ({3+1}/2,{3+4}/2) = (2/2, 1/2)= (1,1/2).
Important Notes
The following points are the important properties of the midpoints.
 The midpoint divides a line segment in an equal ratio, that is, 1:1
 The midpoint divides a line segment into two equal parts.
 The bisector of a line segment cuts it at its midpoint.
Formulas Related to Midpoint
The midpoint formula includes computations separately for the xcoordinate of the points, and the ycoordinate of the points. Further the computations of points between two given points, also include similar computation of the xcoordinate and the ycoordinate of the given points. The following two formulas are closely related to the midpoint formula.
 The Centroid of the Triangle
 The Section Formula
Centroid of a Triangle
The point of intersection of the medians of a triangle is called the centroid of the triangle. The median is a line joining the vertex to the midpoint of the opposite side of the triangle. The centroid of the triangle is equal to the sum of the xcoordinates of the vertices of the triangle divided by 3, and the sum of the ycoordinates of the vertices of the triangle divided by 3. The centroid divides the median of the triangle in the ratio 2:1. For a triangle with vertices (x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3}) the formula to find the coordinates of the centroid of the triangle is as follows.
Section Formula
The section formula is helpful to find the coordinates of any point which is on the line joining the two points. Further, the ratio in which the point divided the line joining the two given points is needed to know the coordinates of the point. The point can be located between the points, or anywhere beyond the points, but on the same line. The section formula to find the coordinates of a point, which divides the line joining the points (x_{1}, y_{1}), and (x_{2}, y_{2}) in the ratio m:n is as follows. The positive sign is used in the formula to find the coordinates of the point, which divides the points internally, and the negative sign is used if the point is dividing externally.
Solved Examples on Midpoint

Example 1: The diameter of a circle has endpoints, (2, 3) and (6, 5). Find the coordinates of the center of the circle.
Solution:
The center of a circle divides the diameter into 2 equal parts. So, it is a midpoint of the diameter. Let x_{1}=2, y_{1}=3, x_{2}= 6, and y_{2} = 5 The coordinates of the center is calculated as: {(x_{1} + x_{2})/2, (y_{1} + y_{2})/2} = {(2 + 6)/2. (3 + 5)/2} = (4/2, 1/2) = (2, 1). Therefore, the center of the circle is (2, 1).

Example 2: Consider the line segment \(\overline{AB}\) shown below.
The endpoints are (1, h) and (5, 7). Find the value of h if the midpoint of \(\overline{AB}\) is (3, 2).
Solution:
Let x_{1}=1, y_{1}=h, x_{2}=5, and y_{2}=7. According to the definition of midpoint we have, {(x_{1} + x_{2})/2, (y_{1} + y_{2})/2} = {(1 + 5)/2. (h + 7)/2} = (6/2, (h + 7)/2) = (3, (h + 7)/2). Equalizing this with the midpoint value (3, 2) we have (h + 7)/2 = 2; h + 7 = 2 × 2; h + 7 = 4; h = 4 7; h = 11. Therefore, the value of h is 11.
FAQs on Midpoint
Can Midpoint Be a Fraction?
Yes, The midpoint value can also be a fraction. It is basically dependent on the numeric value of the two points. The midpoint is the sum of the numeric value of two points, divided by 2. For points such as 4 and 5 on the number line, the midpoint is +1/2.
How Do you Find Midpoint?
The midpoint can be found with the formula {(x_{1} +x_{2})/2, (y_{1} + y_{2})/2}. Here (x_{1}, y_{1}), and (x_{2}, y_{2}) are the coordinates of two points, and the midpoint is a point lying equidistant and between these two points.
What is the Midpoint Formula in Words?
The midpoint formula in words can be described as half of the sum of the xcoordinates of the two points and half of the sum of the ycoordinates of the two points. This is with reference to the midpoint of the line joining two points, whose coordinates are given.
Can the Midpoint be Zero?
The midpoint can be zero. This is dependent on the value of the two points. For two points on a number line on points with values 4, and 4, the midpoint is 0. And for two points such as (2, 5), and (2, 5), the midpoint is equal to (0, 0).
What is the Midpoint of a Line?
The midpoint of a line is a point that is equidistant from the endpoints of the line and in the middle of the line. If the endpoints of the line are (x_{1}, y_{1}), and (x_{2}, y_{2}), then the formula for the midpoint of the line is {(x_{1} +x_{2})/2, (y_{1} + y_{2})/2}.
What is Midpoint of a Curve?
The midpoint of a curve is the midpoint of the largest chord which can be drawn for the curve. The midpoint of a circle is the midpoint of its largest chord, which is the diameter of the circle.
What are Coordinate Axes?
The coordinate axis is a system of representation of a point in a twodimensional plane. It has horizontal axes called the xaxis and vertical axes called the yaxis. The point of intersection of these coordinate axes is the origin. The coordinates of the origin are (0, 0), and any point is represented as (x, y).
What Is the Midpoint of a Triangle?
The midpoint of the triangle is the centroid of the triangle. The centroid is the point of intersection of medians of a triangle. The center of gravity of any triangularshaped object is at its centroid.
What Is the Midpoint of a Circle?
The midpoint of a circle is the center of the circle. The largest chord of the circle is the diameter, and the midpoint of the diameter of the circle is the midpoint of the circle. The midpoint of the circle is equidistant from every point on the circle.