Distance and Mid-Point Formulas

This section has the following videos:

  • Lesson Video
  • Example Set A Practice Problems (Video Solutions)
  • Example Set B Practice Problems (Video Solutions)
  • Example Set C Practice Problems (Video Solutions)

Put away the tape measure- if you want to find the distance between two points (x, y) we can break out the “distance formula”. The formula relates to geometry but it’s huge in algebra.  The formula is pretty easy to use and although it looks a little complex it’s really not.  Let’s say I want to know the distance between the points (2, 5) and (7, 10). The distance formula first tells us to subtract the x coordinates so in this case that would be 2 and 7 or 2-7=-5. Then we subtract the y coordinates so that would be 5 – 10 or -5.  Ok we now square these results and add them so that would be 25 + 25 =50.  Lastly we take the square root of that result and that’s the distance between the points- in this example the distance between the two points is the square root of 50.  Ok get ready to get your algebra skills on with the distance formula!



Wow! another formula to remember in algebra- just what you wanted.  However sad you might be at learning more formulas the mid-point formula is pretty easy.  The formula tells you the location (a point) that’s “mid way” between two other points. Like any formula make sure you understand how to plug in the correct values.


Key concepts to remember:

* the “mid-point” is a (x, y) ordered pair that is half-way between two other points
* make sure to use the formula correctly and don’t make simple mistakes when adding coordinates (common mistakes are incorrectly adding positive and negative numbers)