00:00In this lesson, we're going
00:00to look at the midpoint
00:01of a line segment. So
00:02here is the formula in
00:05the formula booklet. It is
00:07given in the x, y,
00:08and z plane. But I'm
00:09going to show you two
00:10examples. One where we just
00:12look at the x, y
00:13plane, and then the next
00:13one with the z plane.
00:15It's fairly straightforward. But I
00:19just want to go through
00:20and make sure you understand
00:21it. So let's look at
00:22this example. This is similar
00:23to our distance example. I
00:25want to find the midpoint
00:26between these, the midpoint of
00:28the line segment joining these
00:30two points. So basically the
00:31midpoint somewhere here. Now let's
00:34see if we can just
00:35kind of figure it out.
00:37Let's see if we can
00:37just kind of guess it.
00:38Well, the midpoint will be
00:41halfway between here and here,
00:43and then halfway between here
00:45and here. And that's what
00:46this form is. It's x1
00:47plus x2 divided by 2.
00:49It'll give us halfway between
00:51negative 1 and 4. And
00:53then it'll give us for
00:54the y -coordinate halfway between
00:567. So I think I
00:57can actually just figure out
00:58my head. Halfway between negative
01:001 and 4 would be
01:031 .5 because 1 .5
01:07plus 2 .5 is 4
01:08and 1 .5 minus 2
01:10.5 is negative 1. And
01:11what's halfway between 3 and
01:137? Well, that's going to
01:15be 5. So that's my
01:19answer. But let's apply the
01:21formula to make sure
01:24we understand how to do
01:25it. So the formula for
01:26the midpoint is x1 plus
01:29x2 over 2, comma y1
01:33plus y2 over 2. And
01:36this equals in our situation
01:39negative 1 plus 4. So
01:42this is our x1 and
01:44this is our x2. So
01:46minus 1 negative 1 plus
01:474, all divided by 2,
01:51comma
01:523 is y1 plus 7
01:56all over 2 which gives
01:58me 3 divided by 2
02:00is 1 .5 and 3
02:03plus 7 is 10 divided
02:05by 2 is 5, 4,
02:06and 0 .5, 5 which
02:07is what I had. So
02:09it's fairly straightforward. In two
02:12dimensions. In three dimensions it's
02:15not a whole lot more
02:16difficult to be honest but
02:18it is important that we
02:19understand
02:20the x, y and the
02:21z and what the z
02:22actually means. So I'm going
02:24to do the formula is
02:25x1 plus x2 over 2,
02:29comma y1 plus y2 over
02:342, comma z1 plus z2
02:38over 2. And I bracketed
02:40now I just sub in
02:41all these things. Now before
02:45we do it let's have
02:46a look at
02:48geodebra. Now I've put in
02:52the two points here. So
02:54remember you can go here
02:55to geodebra .org if you
02:57want to play around. I've
02:59put in my two points
03:00A, B. There's three negative
03:01four, one, and five, two
03:04negative four. The x -axis
03:07is the red one. The
03:09y -axis is the green
03:10one, and then the z
03:11-axis, the one that comes
03:12straight up, is the blue
03:15one. So if I want
03:16to find
03:16the midpoint, well geodebar has
03:18a nice feature here, I
03:19can just click midpoint and
03:22then it says select two
03:23points. So I'm going to
03:24select B and A and
03:27there it gives me the
03:27midpoint just like that and
03:29it's negative one, negative one,
03:31negative one point five. And
03:33look, it's going to do
03:34this, see what it means
03:36in three dimensions. That's where
03:38it is. It's right between
03:41the two of them.
03:44So please go on to
03:46geodubr and have a play
03:47around to try and understand
03:51coordinates in 3d. Now let's
03:54go back to this. So
03:56it's a case of subbing
03:57in the numbers that I
04:00have. So x1 is 3.
04:02So it's 3 minus 5
04:04over 2 comma negative 4
04:07plus 2 over 2. This
04:09is my negative 4 plus
04:102 over 2 comma 1
04:12minus 4 over 2. I
04:17can already see this is
04:183 minus 5 is negative
04:192 over 2 is negative
04:211. Negative 4 plus 2
04:23is negative 2 divided by
04:242 is negative 1. And
04:261 minus 4 is negative
04:283 divided by 2 is
04:30negative 1 .5, which is
04:34exactly what geodrg were got
04:37negative 1, negative 1, negative
04:391 .5.
04:40So that is how to
04:42get the midpoint in three
04:44dimensions and here in two
04:47dimensions and your formula booklet
04:49is nicely given in the
04:53formula booklet.