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Midpoint Calculator
This calculator finds the midpoint between two points in two or three-dimensional space. The calculator can also determine the endpoint of a line segment given its midpoint and one endpoint.
How to calculate a midpoint of a line segment?
To find midpoint between points A(x1, y1) and B(x2, y2), we usually use formula:
M((x1+x2)/2 , (y1+y2)/2)
Example:
Find the midpoint coordinates of the line segment AB with endpoints (12, 3) and (6, 7)?
Solution:
In this example the constants x1, y1, x2 and y2 are x1 = 12, y1 = 3, x2 = 6, y2 = 7.
M((x1+x2)/2, (y1+y2)/2)
M((12+6)/2, (3+7)/2)
M(18/2, 10/2)
M(9, 9)
Hence, the midpoint of the segment AB is M(9, 9).
Calculating a midpoint in 3D?
The midpoint formula in three dimensions is similar to the two-dimensional case.
M((x1+x2)/2 , (y1+y2)/2, (z1+z2)/2)
Example:
Find the midpoint coordinates given the endpoints are (-3, 4, 6) and (2, 1, 12)?
Solution:
Since the points are in space we need to find six constant: x1, y1, z1, x2, y2 and z2 x1 = -3, y1 = 4, z1 = 6, x2 = 2, y2 = 1, z2 = 12. Now we can apply midpoint formula.
M((x1+x2)/2, (y1+y2)/2, (z1+z2)/2)
M((-3+2)/2, (4+1)/2, (6+12)/2)
M(1/2, 5/2, 9)
Hence, the midpoint is M(1/2, 5/2, 9).
How to find endpoint?
The easiest way to find endpoint is by using formulas:
x2 = 2 xm - x1
y2 = 2 xm - y1
Example:
Find the endpoint if the middle point is M(4,7) and the second endpoint is A(-2,1)
x2 = 2 xm - x1 = 2 * 4 - (-2) = 8 + 2 = 10
y2 = 2 ym - y1 = 2 * 7 - 1 = 14 - 1 = 13.
Hence, the endpoint is B(10, 13).