Midpoint Formula
Basically the midpoint formula is the average of the two x coordinates of the given line
segment and the average of the two y coordinates of the given line segments.
Let's try an example, please copy this example into your notebook!
Ex. 1 Find the midpoint of the line segement joining the points (4,7) and (2,5)
Solution:
Since we are finding the midpoint we have to use the midpoint
formula:
Now substituting the given coordinates into the formula we get:
Simplifying we get:
Our final answer is:
Now let's look at another example.
Ex. 2
In the above example we see that sometimes we get a fractional answer. That's okay!
Remember, fractions are our friends, don't be scared of them!
Now what if the given information is changed somewhat. What if we are given one
endpoint of a line segement, the midpoint of the line segement, and asked to find the
other endpoint. To see a problem like this, copy example3 into your notebook.
Ex. 3 M is the midpoint of line segment AB. The coordinates of A
are (3,7) and the coordinates of M are (6,2). Find the coordinates
of B.
Solution:
This question may seem more difficult to you, however it is really
quite simple if you recall the definition of a midpoint. The
midpoint of a line segment is the average of the x coordinates of
the endpoints and the average of the y coordinates of the
endpoints. Let's give B the coordinates (x,y). Therefore from our
definition of a midpoint we can write:
Solving the first equation will give us the x coordinate of B and
solving the second equation will give us the y coordinate of B.
Now solve the two equations and check your answer below.
9,-3
For more online questions in regards to finding midpoints, click here. (solutions are
provided for this questions)
Now that we know how to find the midpoint of a line segement, let's look at how we can
find the distance of a line segement. This concept along with the midpoint concept will be
used again when you study concis in Math C30. To find the distance between two points
we use what is called the distance formula.
The Distance Formula
Now copy this example down that shows how to use the distance formula.
Ex. 4 Find the distance from point A(-3.7) and point B(5,-1)
Solution: