by
Mr. White
Foundationsl of Mathematics Instructor
Southern California
Vocabulary -
Midpoint
Coordinate/ ordered pair
X-
Y-
Line Segment
Endpoints
Average
Coordinate Geometry
The Midpoint Formula is used in coordinate geometry to allow us to determine the middle coordinate of a line segment. This point is also called the line bisector. It is as if you were measuring a line segment with a ruler. The middle of the line segment would be the midpoint.
For example, given two points, A (0,0) and B (4,3), what is the midpoint of the line that connects the two points, line segment AB? We could draw the line on a coordinate graph, but that is not necessary. We can use the Midpoint Formula, instead. This formula requires you to add the two X coordinates and average them. Then, add the two y coordinates, and average them. Those two answers are put together in the form of an ordered pair, which is the location of the line segment's middle point.
A (0, 0) B ( 4 , 4).
Calculate the midpoint of segment AB:
(4 + 0) /2 , (4 + 0)/2
This leads to the next step:
4/2, 4/2
which is the midpoint,
( 2, 2 )
Try another example.
Given the two points, R (1,2) and P (6, 5), what is the midpoint of the line segment, PR?
Solution: Add the x- coordinates, and divide by two, for the x-coordinate of the midpoint. Add the y- coordinates, and divide by two, for the y-coordinate of the midpoint.
Calculate the midpoint:
(1 + 7) / 2 , (2 + 6) / 2
This leads to the next step:
8/2, 8/2
or
(4, 4)
For more examples, go to these websites:
http://www.purplemath.com/modules/midpoint.htm
http://cs.selu.edu/~rbyrd/math/midpoint/
http://teacherschoice.com.au/Maths_Library/Analytical%20Geometry/Alg_16.htm
http://www.ronblond.com/M10/mid/index.html (A very interesting applet)
