Recall that the midpoint's  and  values are the average of the  and  values of the two points in question.   Thus, if we call the other point , we know that:

 and 

Solve each equation accordingly:

For , multiply both sides by :

Thus, 

The same goes for the other equation:

, so 

Thus, our point is  

If  is the midpoint of  and another point, what is that other point?

Recall that the midpoint's  and  values are the average of the  and  values of the two points in question. Thus, if we call the other point , we know that:

 and 

Solve each equation accordingly:

For , multiply both sides by  and then subtract  from both sides:

Thus, 

For , multiply both sides by 2 and then subtract 10 from both sides: 

Thus, 

Thus, our point is 

The midpoint formula is 

The midpoint formula is equal to . Add the x-values together and divide them by 2, and do the same for the y-values.

x: (2 + 8) / 2 = 10 / 2 = 5

y: (6 + 4) / 2 = 10 / 2 = 5

The midpoint of MN is (5,5).

The midpoint formula is  . An easy way to remember this is that finding the midpoint simply requires that you find the averageof the two x-coordinates and the average of the two y-coordinates. In this case, the two x-coordinates are 3 and 7, and the two y-coordinates are 5 and 9. If we substitute these values into the midpoint formula, we get (3 + 7/2), (5 + 9)/2, which equals (5, 7). If you got (–2, –2), you may have subtracted your x and y-coordinates instead of adding. If you got (10,14), you may have forgotten to divide your x and y-coordinates by 2. If you got (6,6), you may have found the average of x_{1 and} y₂ and x₂ and y₁ instead of keeping the x-coordinates together and the y-coordinates together. If you got (7, 5), you may have switched the x and y-coordinates.

The formula for midpoint = (x₁ + x₂)/2, (y₁ + y₂)/2. Substituting in the two x coordinates and two y coordinates from the endpoints, we get (–1 + 3)/2.

(4 + 6)/2 or (1, 5) as the midpoint.

To solve this problem we use the midpoint formula.  We find the average of the x and y coordinates.  (–6 + 4)/2, (4 + –6)/2 = –1, –1

Method A:

To find the midpoint, draw the number line that contains points  and .  

Then calculate the distance between the two points.  In this case, the distance between  and  is .  By dividing the distance between the two points by 2, you establish the distance from one point to the midpoint.  Since the midpoint is 12 away from either end, the midpoint is 5.

Method B:

To find the midpoint, use the midpoint formula:

Translating the intersections into points on a graph, Janice works at (33,7) and Mark works at (15,5). The midpoint of these two points is found by taking the average of the x-coordinates and the average of the y-coordinates, giving ((33+15)/2 , (5+7)/2) or (24, 6). Traveling in one direction at a time, the number of blocks from either office to 24^th street is 9, and the number of blocks to 6^th is 1, for a total of 10 blocks.

On the number line, is  units away from .

We find the midpoint of this distance by dividing it by 2.

To find the midpoint, we add this value to the smaller number or subtract it from the larger number.

The midpoint value will be .