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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