Midpoint Formula Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

easy
A circle has diameter endpoints A(−6,2)A(-6, 2) and B(4,10)B(4, 10). Find the coordinates of the centre of the circle.

Solution

  1. 1
    The centre of a circle is the midpoint of any diameter.
  2. 2
    Apply the midpoint formula: (−6+42,2+102)\left(\frac{-6 + 4}{2}, \frac{2 + 10}{2}\right).
  3. 3
    Simplify: (−22,122)=(−1,6)\left(\frac{-2}{2}, \frac{12}{2}\right) = (-1, 6).

Answer

(−1,6)(-1, 6)
A diameter passes through the centre of the circle, so the centre sits exactly halfway between its endpoints. That makes the midpoint formula the right tool for the job.

About Midpoint Formula

A formula for finding the point exactly halfway between two points in the coordinate plane, by averaging their coordinates.

Learn more about Midpoint Formula →

More Midpoint Formula Examples

Example 1 easy

Find the midpoint of the segment joining [formula] and [formula].

Example 2 medium

The midpoint of segment [formula] is [formula]. If [formula], find the coordinates of [formula].

Example 3 easy

Find the midpoint of the segment joining [formula] and [formula].

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