Midpoint

Midpoint
The midpoint of the segment (x1, y1) to (x2, y2)

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.

Contents

Formulas

The formula for determining the midpoint of a segment in the plane, with endpoints (x1) and (x2) is:

 \frac{x_1 + x_2}{2}

The formula for determining the midpoint of a segment in the plane, with endpoints (x1, y1) and (x2, y2) is:

\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)


The formula for determining the midpoint of a segment in the space, with endpoints (x1, y1, z1) and (x2, y2 z2) is:

\left(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2}\right)

More generally, for an n-dimensional space with axes x_1, x_2, x_3, \dots, x_n\,\!, the midpoint of an interval is given by:

\left(\frac{x_{1_1} + x_{1_2}}{2}, \frac{x_{2_1} + x_{2_2}}{2}, \frac{x_{3_1} + x_{3_2}}{2}, \dots , \frac{x_{n_1} + x_{n_2}}{2} \right)

Construction

The midpoint of a line segment can be located by first constructing a lens using circular arcs, then connecting the cusps of the lens. The point where the cusp-connecting line intersects the segment is then the midpoint. It is more challenging to locate the midpoint using only a compass, but it is still possible.[1]

See also

References

External links

  • Animation - showing the characteristics of the midpoint of a line segment