The literal meaning of midpoint is the point that is exactly in the middle of something. In mathematics, the midpoint is the point on a straight line which is exactly at the middle of the straight line joining two endpoints.
In other words, the midpoint is the point on the line that divides the line into two halves. The midpoint of a line is at an equal distance from both the endpoints of that line. A line drawn through the midpoint and perpendicular to a straight line bisects the line which means this line divides the given line into two equal parts.
The midpoint formula is developed by mathematicians to give an idea about the process to be used to find the midpoint between two fixed points on a two-dimensional plane. The steps of the midpoint formula are:
- We have to identify the two endpoints of the given line by their coordinates.
- The midpoint of the line joining these two points will lie at the middle of this line. To locate the midpoint, we have to find the coordinates of the midpoint.
- To find the x-coordinate of the midpoint we will add the x-coordinates of both endpoints divided by 2, and the coordinate of the midpoint will be obtained by adding the y-coordinates of both endpoints divided by 2.
- The x and y coordinate thus obtained indicates the midpoint of the given line.
For example, in the coordinate plane, consider two points A (x=4, y=15) and B (x=16, y=7). Then the x-coordinate and y-coordinate of the midpoint between A and B will be x=10 and y=11 respectively.
The midpoint formula implies that a midpoint is relevant and can be determined only for a line segment that has two fixed endpoints. A line that is indefinite in both directions and a ray which has only one fixed endpoint don’t have any midpoint.
Finding the Midpoint
Let’s consider two points P and Q which are the endpoints of the line PQ and the midpoint of PQ is R. So the point R is just halfway between points P and Q and we can say that PR = QR.
Therefore, to find out the midpoint, we can simply measure the length of the line segment and divide it by 2. The value thus obtained refers to the distance of the midpoint from either of the endpoints. In the above case, the value of PQ/2 gives the distance of midpoint R on the line from any of the endpoints P and Q.
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