what is midpoint formula

Question

Thanks!

Answer 1

Jamika,

 

The position of a point can be expressed as a number or numbers. If you are talking about the midpoint of points on a number line then each point is expressed by one number. The midpoint for two points is the same as taking the average of the number that represent the points. So if you had 5 and 13 on the number line you would take the average (5 + 13)/2. So the midpoint would be nine.

When you plot points in two or more dimensions multiple numbers are used for each point. To find the mid point you would pair the numbers from each point in order. You would do exactly what you do with the number line except instead of getting one number you would get the same number of values that was used to represent each point. So the mid point of (5, 2) and (13, 12) is ((5+13)/2, (2 + 12)/2) or (9, 8).

I guess this would make the mid point formula ((x₁₊x₂)/2, ...) where the "..." stands for any doing it again for any additional dimensions that you need. 

Answer 2

For the points (x₁, y₁ and (x₂, y₂), the midpoint is 

 

( (x₁+x₂)/2, (y₁+y₂)/2 )