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# The midpoint of a line segment. Working out the middle of 2 coordinate points.

The midpoint is located in the middle of a line segment. So if you have the two coordinates of the ends of the line segment, then the midpoint can be calculated by adding up both the x and y coordinates and halving these totals.

**Example 1**

The diagram shows the line segment AB, where A = (2,4) and B = (8,9). What is the coordinate of the midpoint of the line segment?

First find the x-coordinate midpoint. Do this by adding up the x coordinates and halving the answer:

½ of (2+8)= ½ of 10 = 5

Next find the midpoint of the y coordinates. This time half the total of the y coordinates:

½ of (4+9) = ½ of 13 = 6.5

So the midpoint of the line segment AB is (5,6.5).

**Example 2**

The diagram shows the line segment PQ, where P = (-5,-3) and Q = (7,8). What is the coordinate of the midpoint of the line segment?

First find the x-coordinate midpoint. Do this by adding up the x coordinates and halving the answer:

½ of (-5+7)= ½ of 2 = 1

Next find the midpoint of the y coordinates. This time half the total of the y coordinates:

½ of (-3+8) = ½ of 5 = 2.5

So the midpoint of the line segment AB is (1,2.5).

**Example 3**

Two coordinates A and B are plotted onto a grid. Point A is at (-3,-9) and point B is at (-1,5). The two points are joined together with a straight line. Write down the coordinate point of the middle of the line?

Just like the previous 2 examples, all the question is asking you to do is to work out the midpoint of the line segment AB.

First find the x-coordinate midpoint. Do this by adding up the x coordinates and halving the answer:

½ of (-3+-1)= ½ of -4 = -2

Next find the midpoint of the y coordinates. This time half the total of the y coordinates:

½ of (-9+5) = ½ of -4 = -2

So the pint in the middle of A and B is (-2,-2).

So working out the midpoint of a line segment is quite a straight forward process. Just remember to find the average of the x and y coordinates.