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[Music]
in today's video we're going to cover
how to find the midpoint of a line
or the midpoint between two sets of
coordinates
for example the midpoint of a line
segment like this which stretches from 2
3 to 6 9.
now the midpoint is exactly what it says
it is
it's just the point that's right in the
middle of two pairs of coordinates
or right in the middle of the line
so in this example to find the x
coordinates of the midpoint
we just need to find what's in the
middle of two and
which is 4.
and to find the y-coordinate of the
midpoint
we just need to find what's in the
middle of 3 and 9
which is 6.
so the midpoint of this line is 4 6.
now this one here was a fairly easy
example and we had the graph to help us
in exams though you might not have the
graph
and the numbers involved might be a bit
more
complicated so a better technique to
find the midpoint is to use this formula
instead
it works in basically the same way by
finding the average of the x values and
the average of the y values
but before we can use it we need to
label our two points
so we pick one of them to be the first
and label the coordinates x1 y1
and the other point to be the second and
label the coordinates x2 y2
although it doesn't matter which point
is the first and which point is the
second
then to use our formula all we have to
do is plug in the numbers
so we start by adding together x1 and x2
which would be 2 plus 6
and then we divided by 2 to get the
average of those two x coordinates which
will be 4.
and so we know that the x coordinate of
our midpoint is 4.
then we do exactly the same thing with
the two y values
so we do 3 plus 9
divided by 2
which is 6.
so that's the y-coordinate of our
midpoint
and notice that we've got a final answer
of 4 6
just like we did when we used the graph
method a minute ago
now if we take a closer look at this
formula for a moment
you might notice that it's actually
written like a pair of coordinates
which is why it has the brackets on the
sides and the comma in the middle
so this left part is basically a mini
formula to work out the x coordinates of
the midpoint
by finding the average of our x values
and this right part is a mini formula to
work out the y coordinates by finding
the average of our y values
so this is why we just plug everything
straight in and when we simplify it we
end up with the coordinate that we need
let's try one more question from scratch
this time
so here we're looking for the midpoint
between minus six two
and seven minus eight
the first thing you want to do here is
write out the formula
and label your coordinates x1 y1
and x2 y2 then you can go straight ahead
and plug the numbers into the formula
so minus 6 plus 7 over 2 to find our x
coordinate
then a comma
and then 2 plus minus 8 all over 2 to
find our y coordinate
then you can simplify it
to 1 over 2
comma minus 6 over 2
and that leaves us with a midpoint of
one half comma negative three
one thing to mention here though is that
because our x coordinate wasn't a whole
number this time
it's up to you whether you want to leave
it as a fraction or change it to a
decimal
so we could also have written our answer
as 0.5 negative 3.
that's everything for this video though
so thanks for watching and see you again
soon
