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Let's say I have the point 3 comma negative 4.

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So that would be 1, 2, 3, and then down 4.

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1, 2, 3, 4.

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So that's 3 comma negative 4.

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And I also had the point 6 comma 1.

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So 1, 2, 3, 4, 5, 6 comma 1.

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So just like that.

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6 comma 1.

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In the last video, we figured out that we could just use the

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Pythagorean theorem if we wanted to figure out the

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distance between these two points.

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We just drew a triangle there and realized that this was the

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hypotenuse.

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In this video, we're going to try to figure out what is the

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coordinate of the point that is exactly halfway between

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this point and that point?

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So this right here is kind of the distance, the line that

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connects them.

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Now what is the coordinate of the point that is exactly

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halfway in between the two?

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What is this coordinate right here?

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It's something comma something.

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And to do that-- let me draw it really big here.

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Because I think you're going to find out that it's actually

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pretty straightforward.

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At first it seems like a really tough problem.

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Gee, let me use the distance formula with some variables.

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But you're going to see, it's actually one of the simplest

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things you'll learn in algebra and geometry.

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So let's say that this is my triangle right there.

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This right here is the point 6 comma 1.

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This down here is the point 3 comma negative 4.

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And we're looking for the point that is smack dab in

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between those two points.

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What are its coordinates?

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It seems very hard at first. But it's easy when you think

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about it in terms of just the x and the y coordinates.

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What's this guy's x-coordinate going to be?

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This line out here represents x is equal to 6.

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This over here-- let me do it in a little darker color--

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this over here represents x is equal to 6.

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This over here represents x is equal to 3.

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What will this guy's x-coordinate be?

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Well, his x-coordinate is going to be smack dab in

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between the two x-coordinates.

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This is x is equal to 3, this is x is equal to 6.

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He's going to be right in between.

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This distance is going to be equal to that distance.

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His x-coordinate is going to be right in between

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the 3 and the 6.

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So what do we call the number that's right in between

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the 3 and the 6?

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Well we could call that the midpoint, or we could call it

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the mean, or the average, or however you want

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to talk about it.

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We just want to know, what's the average of 3 and 6?

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So to figure out this point, the point halfway between 3

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and 6, you literally just figure out, 3 plus 6 over 2.

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Which is equal to 4.5.

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So this x-coordinate is going to be 4.5.

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Let me draw that on this graph.

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1, 2, 3, 4.5.

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And you see, it's smack dab in between.

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That's its x-coordinate.

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Now, by the exact same logic, this guy's y-coordinate is

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going to be smack dab between y is equal to negative 4 and y

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is equal to 1.

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So it's going to be right in between those.

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So this is the x right there.

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The y-coordinate is going to be right in between y is equal

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to negative 4 and y is equal to 1.

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So you just take the average.

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1 plus negative 4 over 2.

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That's equal to negative 3 over 2 or you could say

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negative 1.5.

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So you go down 1.5.

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It is literally right there.

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So just like that.

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You literally take the average of the x's, take the average

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of the y's, or maybe I should say the mean to be a little

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bit more specific.

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A mean of only two points.

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And you will get the midpoint of those two points.

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The point that's equidistant from both of them.

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It's the midpoint of the line that connects them.

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So the coordinates are 4.5 comma negative 1.5.

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Let's do a couple more of these.

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These, actually, you're going to find are very, very

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straightforward.

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But just to visualize it, let me graph it.

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Let's say I have the point 4, negative 5.

94
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So 1, 2, 3, 4.

95
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And then go down 5.

96
00:04:05,099 --> 00:04:08,159
1, 2, 3, 4, 5.

97
00:04:08,159 --> 00:04:10,419
So that's 4, negative 5.

98
00:04:10,419 --> 00:04:11,959
And I have the point 8 comma 2.

99
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So 1, 2, 3, 4, 5, 6, 7, 8 comma 2.

100
00:04:17,100 --> 00:04:18,410
8 comma 2.

101
00:04:18,410 --> 00:04:20,149
So what is the coordinate of the midpoint

102
00:04:20,149 --> 00:04:20,899
of these two points?

103
00:04:20,899 --> 00:04:23,600
The point that is smack dab in between them?

104
00:04:23,600 --> 00:04:26,970
Well, we just average the x's, average the y's.

105
00:04:26,970 --> 00:04:30,020
So the midpoint is going to be-- the x values are 8 and 4.

106
00:04:30,019 --> 00:04:33,259
It's going to be 8 plus 4 over 2.

107
00:04:33,259 --> 00:04:35,659
And the y value is going to be-- well, we have a 2 and a

108
00:04:35,660 --> 00:04:36,510
negative 5.

109
00:04:36,509 --> 00:04:40,219
So you get 2 plus negative 5 over 2.

110
00:04:40,220 --> 00:04:41,460
And what is this equal to?

111
00:04:41,459 --> 00:04:48,750
This is 12 over 2, which is 6 comma 2 minus 5 is negative 3.

112
00:04:48,750 --> 00:04:53,279
Negative 3 over 2 is negative 1.5.

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00:04:53,279 --> 00:04:58,609
So that right there is the midpoint.

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00:04:58,610 --> 00:05:01,040
You literally just average the x's and average the y's, or

115
00:05:01,040 --> 00:05:01,660
find their means.

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00:05:01,660 --> 00:05:02,820
So let's graph it, just to make sure

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it looks like midpoint.

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6, negative 5.

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1, 2, 3, 4, 5, 6.

120
00:05:08,199 --> 00:05:09,519
Negative 1.5.

121
00:05:09,519 --> 00:05:11,519
Negative 1, negative 1.5.

122
00:05:11,519 --> 00:05:13,099
Yep, looks pretty good.

123
00:05:13,100 --> 00:05:16,020
It looks like it's equidistant from this point and

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that point up there.

125
00:05:17,550 --> 00:05:19,090
Now that's all you have to remember.

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Average the x, or take the mean of the x, or find the x

127
00:05:21,485 --> 00:05:22,840
that's right in between the two.

128
00:05:22,839 --> 00:05:23,799
Average the y's.

129
00:05:23,800 --> 00:05:25,050
You've got the midpoint.

130
00:05:25,050 --> 00:05:28,160
What I'm going to show you now is what's in many textbooks.

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00:05:28,160 --> 00:05:33,530
They'll write, oh, if I have the point x1 y1, and then I

132
00:05:33,529 --> 00:05:36,250
have the point-- actually, I'll just stick it in yellow.

133
00:05:36,250 --> 00:05:38,949
It's kind of painful to switch colors all the time-- and then

134
00:05:38,949 --> 00:05:43,389
I have the point x2 y2, many books will give you something

135
00:05:43,389 --> 00:05:44,899
called the midpoint formula.

136
00:05:44,899 --> 00:05:47,819
Which once again, I think is kind of silly to memorize.

137
00:05:47,819 --> 00:05:49,459
Just remember, you just average.

138
00:05:49,459 --> 00:05:51,779
Find the x in between, find the y in between.

139
00:05:51,779 --> 00:05:53,674
So midpoint formula.

140
00:05:53,675 --> 00:05:57,079


141
00:05:57,079 --> 00:05:59,879
What they'll really say is the midpoint-- so maybe we'll say

142
00:05:59,879 --> 00:06:04,409
the midpoint x-- or maybe I'll call it this way.

143
00:06:04,410 --> 00:06:05,560
I'm just making up notation.

144
00:06:05,560 --> 00:06:10,079
The x midpoint and the y midpoint is going to be equal

145
00:06:10,079 --> 00:06:16,169
to-- and they'll give you this formula. x1 plus x2 over 2,

146
00:06:16,170 --> 00:06:19,580
and then y1 plus y2 over 2.

147
00:06:19,579 --> 00:06:21,069
And it looks like something you have to memorize.

148
00:06:21,069 --> 00:06:22,139
But all you have to say is, look.

149
00:06:22,139 --> 00:06:27,089
That's just the average, or the mean,

150
00:06:27,089 --> 00:06:28,339
of these two numbers.

151
00:06:28,339 --> 00:06:32,039


152
00:06:32,040 --> 00:06:35,050
I'm adding the two together, dividing by two, adding these

153
00:06:35,050 --> 00:06:36,730
two together, dividing by two.

154
00:06:36,730 --> 00:06:37,900
And then I get the midpoint.

155
00:06:37,899 --> 00:06:40,769
That's all the midpoint formula is.

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00:06:40,769 --> 00:06:40,799