Return to the Purplemath home page

 The Purplemath Forums
Helping students gain understanding
and self-confidence in algebra

powered by FreeFind


Return to the Lessons Index  | Do the Lessons in Order  |  Get "Purplemath on CD" for offline use  |  Print-friendly page

The Midpoint Formula (page 1 of 2)

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.

The Midpoint Formula works exactly the same way. If you need to find the point that is exactly halfway between two given points, just average the x-values and the y-values.

  • Find the midpoint between (1, 2) and (3, 6).

    Apply the Midpoint Formula:

      midpoint is (1, -2)

    So the answer is P = (1, 2).

Technically, the Midpoint Formula is the following:

    [(x_1 + x_2)/2 , (y_1 + y_2)/2]

But as long as you remember that you're averaging the two points' x- and y-values, you'll do fine. It won't matter which point you pick to be the "first" point you plug in.

  • Find the midpoint between (6.4, 3) and (10.7, 4).

    Apply the Midpoint Formula:

      P = (-2.15, 3.5)

    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:   Copyright Elizabeth Stapel 2000-2011 All Rights Reserved

      ( [p - 1]/2 , 2.5 ) = ( -2, 2.5 ]

    This reduces to needing to figure out what p is, in order to make the x-values work:

      p = -3

    So the answer is p = 3.

Let's do some more examples....

Top  |  1 | 2  |  Return to Index  Next >>

Cite this article as:

Stapel, Elizabeth. "The Midpoint Formula." Purplemath. Available from Accessed


  Linking to this site
  Printing pages
  School licensing

Reviews of
Internet Sites:
   Free Help
   Et Cetera

The "Homework

Study Skills Survey

Tutoring from Purplemath
Find a local math tutor

This lesson may be printed out for your personal use.

Content copyright protected by Copyscape website plagiarism search

  Copyright 2000-2012  Elizabeth Stapel   |   About   |   Terms of Use


 Feedback   |   Error?