The midpoint (also known as class mark in relation to histogram) is the middle point of a line segment. It is equidistant from both endpoints.
The midpoint of the segment (x1, y1) to (x2, y2)Formulas
The formula for determining the midpoint of a segment in the plane, with endpoints (x1) and (x2) is:
The formula for determining the midpoint of a segment in the plane, with endpoints (x1, y1) and (x2, y2) is:
The formula for determining the midpoint of a segment in the plane, with endpoints (x1, y1, z1) and (x2, y2 z2) is:
More generally, for an n-dimensional space with axes
the midpoint of an interval is given by:
Sometimes you need to find the point that is exactly between two other points. For instance, you might need to find a line that bisects (divides into equal halves) a given line segment. This middle point is called the "midpoint". The concept doesn't come up often, but the Formula is quite simple and obvious, so you should easily be able to remember it for later.
Think about it this way: If you are given two numbers, you can find the number exactly between them by averaging them, by adding them together and dividing by two. For example, the number exactly halfway between 5 and 10 is ^[5 + 10]/2 = 15/2 = 7.5.
Find the midpoint between (–1, 2) and (3, –6).
Apply the Midpoint Formula:
So the answer is P = (1, –2).
Find the midpoint between (6.4, 3) and (–10.7, 4).
Apply the Midpoint Formula:
So the answer is P = (–2.15, 3.5)
Find the value of p so that (–2, 2.5) is the midpoint between (p, 2) and (–1, 3).
I'll apply the Midpoint Formula:
This reduces to needing to figure out what p is, in order to make the x-values work:
So the answer is p = –3.
Reference:
http://en.wikipedia.org/wiki/Midpoint
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