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.