Video Transcript
The coordinates of 𝐴 and 𝐵 are
one, nine and nine, nine, respectively. Determine the coordinates of the
points that divide the line segment 𝐴𝐵 into four equal parts.
So the first thing we’re gonna do
is draw a sketch to help us visualize the problem. So I’ve got a coordinate grid
here. So we’ve got our 𝑥- and
𝑦-axis. Now, what we want to do is mark on
the coordinates of 𝐴 and 𝐵. And when we do that, we’ve got 𝐴
at one, nine and 𝐵 at nine, nine. And then what we’re interested in
is the line segment between them because we want to find the coordinates of the
points that will divide it into four equal parts.
Well, if we’re gonna divide it into
four equal parts, the first thing we want to do is we want to find the midpoint. So how are we going to do that? So, in order to find the halfway
point, we have a formula. And that is that the midpoint is
equal to 𝑥 sub one plus 𝑥 sub two over two, 𝑦 sub one plus 𝑦 sub two over
two. But what we’re gonna do is we’re
gonna use this to find our midpoint. But what we should think is if we
wanna see where our midpoint is, we should notice that it’s gonna be on the line
segment 𝐴𝐵. We should also notice that the one
thing that’s going to be the same on the midpoint as the coordinates 𝐴 and 𝐵 is
going to be the 𝑦-coordinate. And that’s because we have a
horizontal line, so the 𝑦-coordinate never changes. We’ll plug it in to our formula to
see if that is the case.
Well, if we substitute our values
into our formula, we’ve got 𝑥 sub one, 𝑦 sub one and 𝑥 sub two, 𝑦 sub two, that
is, the 𝑥- and 𝑦-coordinates of our two points. So we’re gonna have the midpoint is
equal to one plus nine over two, nine plus nine over two, which is gonna give us the
coordinate five, nine. And that’s because one plus nine is
10. 10 over two is five. And then nine plus nine is 18. 18 over two is nine. As we expected, the 𝑦-coordinate’s
gonna be the same.
So now, we have the midpoint, which
is five, nine. So therefore, that’s one of the
points that divides our line segment 𝐴𝐵 into four equal parts. But now what we want are the other
two points we need to divide it into four parts. And to find them, what we’re gonna
do is find the midpoint between 𝐴 and 𝑚 and then the midpoint between 𝑚 and
𝐵. Well, once again, our 𝑦-coordinate
shouldn’t change. But then, if we’re gonna put it
into our formula, we’re gonna have one plus five over two, nine plus nine over two,
which is gonna give us the coordinate three, nine. And we could’ve worked this out
because if we think about 𝐴 and 𝑚, we’ve got 𝑥-coordinates of one and five. So therefore, halfway between these
is gonna be three. So that gives us our three,
nine.
So now, we have one more point to
find. And that’s between 𝑚 and 𝐵. So once again, we can plug it into
the formula. However, all we need to really do
is find what the midpoint between five and nine are because they’re the
𝑥-coordinates of 𝑚 and 𝐵. Well, the midpoint between five and
nine is seven. So we get seven, nine. We also
worked out again using the formula because five plus nine is 14. 14 over two is seven. So there we have it. We have our three points that
divide the line segment 𝐴𝐵 into four equal parts. They are five, nine; three, nine;
and seven, nine.
