Up next in 10
How to Use the Distance Formula (With Real Life Examples)
0 views
May 21, 2025
In this video, we dive deep into the Distance Formula and how it's used to find the distance between two points on a coordinate plane. But we’re not just doing boring math—we’re talking drones, war zones, GPS, and park trails to make it real and relatable. Learn: What the distance formula is How to apply it step-by-step Why it's useful beyond the classroom (yes, even in war movies and GPS apps!) How to find the perimeter of a triangle using multiple applications of the formula
View Video Transcript
0:00
so we are talking about the distance
0:02
formula right the distance formula in
0:05
this chapter we're going to learn how to
0:06
find the distance between two points
0:09
given their coordinates all right given
0:11
their coordinates we're going to find
0:13
the distance now uh when it comes to
0:15
like when do you use like in war or when
0:18
people go on like a campaign they're
0:19
trying to fight they have like
0:21
coordinates this is how they figure out
0:22
the distance they can use the distance
0:24
from figure out the distance if I'm
0:26
going to attack this place here I have
0:28
the coordinates I have the coordinates
0:30
So I'm like okay we can figure out the
0:31
distance and then we communicate that to
0:33
the drone and the drone does what it
0:35
drops those things boom boom boom and
0:36
then So we can use that right we can use
0:39
this kind of stuff we can use this to
0:41
find distance so example let's say you
0:45
have somebody that's like walking in the
0:47
park okay they're walking and they're
0:49
like biking on the trail or maybe
0:51
walking in the park and they're trying
0:52
to figure out how do I go from this
0:54
point to this point or this point to
0:56
this point how do you figure it out if
0:58
you don't actually know now we know that
1:00
what kind of triangle is this
1:03
right triangle right now what is
1:05
different between what we did here and
1:07
what we did before in this case what do
1:09
we have you have all
1:11
the ordered pairs i have ordered pairs
1:14
do I have the distances between the two
1:16
legs i do not have it i only have the
1:19
coordinates of the points right and how
1:22
do I figure out the distance if I don't
1:24
have the actual u measurement i'm going
1:27
to use the distance formula that's what
1:29
this comes in handy so we're going to
1:30
learn the distance formula all right so
1:33
for example if I have two points
1:35
A who has which has like this
1:39
coordinates here X1 Y1 and B has X2 Y2
1:43
these are the coordinates right if I
1:44
want to find the distance between A and
1:46
B this is the formula that I'm going to
1:48
use here right is the square root of x1
1:51
- x2 plus the square + y1 - y2 so the
1:57
square root of that will give me the
1:58
distance between any given point excuse
2:01
me we need to know anything about C uh
2:04
right now I'm not interested in C right
2:06
because I just want to find the distance
2:08
between A and B okay if I wanted to find
2:10
the distance between A and C I would
2:12
still use the same formula a and B are
2:14
just arbitrary point that I'm I'm using
2:16
it's not like typically I'm not really
2:18
doing it for this problem i'm just
2:19
giving you a general formula right this
2:22
is the general formula so now we're
2:24
going to do an example and it's going to
2:26
make sense yeah um why are we having the
2:28
square root of two um over x1 - x2 why
2:32
are we having a square root yes we want
2:34
to find the distance between the two
2:35
points right if I have a point here let
2:39
me let me draw this right let me draw
2:41
this you guys remember how to put uh
2:44
points on the coordinate of axis right
2:47
so -2 one so x is -2 y is what one it's
2:51
going to be here right so a is -2 1 and
2:56
then b is 4 three so 1 2 3 4 and then uh
3:00
1 2 and three so I'm here b is right
3:04
here four and three so I want to know
3:06
how far A is from B how am I going to
3:09
figure it out am I going to come here
3:10
and I'm going to take my uh some kind of
3:13
a ruler and try to figure out the
3:14
measure let me see that's not what I'm
3:16
going to do right i'm not going to do
3:18
that i'm going to use the distance
3:20
formula because now we are getting
3:22
introduced to it so I'm going to use the
3:24
distance formula so my goal is to figure
3:27
out how to apply this formula to any
3:30
given point that I would have yeah
3:34
why does this formula work that's a
3:36
great question somebody came up with
3:39
this formula now you're asking me the
3:41
the the why behind it i can talk to you
3:44
about it later on not today right so you
3:46
have the good question i'm going to talk
3:48
to you about that later on so this
3:49
formula works because it's also part of
3:52
the it's not really the pagonal theorem
3:54
but you can pretty much figure out the
3:56
distance between two given uh the
3:58
quantity why does it work i never really
4:00
investigated that but I need to do that
4:01
that's a good question mr
4:05
me as a student i will ask you
4:06
everything with math why interesting so
4:11
I want to see you probably
4:14
in if I'm in a world where I could use
4:16
this
4:18
i'm going to be trying to these are the
4:21
coordinates if you want to figure out
4:22
how to get from point A to point B and
4:24
all you have is coordinates so how you
4:26
going to figure it out are you going to
4:28
try now listen to this you are you going
4:30
to try to figure out the distance by by
4:32
going no you're not going to do that you
4:34
figure out the coordinates right and
4:35
then you you pass on the coordinate you
4:37
remember in war what did they do snipers
4:40
right the sniper they say "All right
4:41
we're going to figure this out." So they
4:43
get all these things okay they go "Hey
4:44
Alpha is located in LZPT." What they use
4:47
all these codes and stuff they give you
4:49
the coordinates and then the guy goes
4:51
"All right Roger that." And he go and
4:55
then he goes
4:58
"Fense." Love you know like I love his
5:00
movies when I watch him i'm a W movie i
5:03
love it i love Woo yeah me too but
5:09
some little he
5:15
[Music]
5:16
I'm not afraid
5:18
maybe someday you're going to use it you
5:20
never know never say you you don't want
5:23
to
5:28
that's why he said right that's why he's
5:31
here what about other than war what am I
5:33
going to use this for what if your
5:35
GPS and you need Oh how do you think
5:38
they go to freaking farms how do you
5:41
think now this is funny how do you think
5:44
your GPS came by coordinates they use
5:48
all this coordinate they put it in there
5:49
this is how they all somebody had to do
5:51
it for you right somebody had to do it
5:54
and now you're benefiting from it so if
5:56
those people are like
5:58
I we'll never have what we have okay
6:01
true
6:02
true people who actually thank those
6:05
people for like taking the time to study
6:07
these things and then give us the
6:08
benefit
6:10
making you suffer all right try to get
6:12
to Emily's house and say my address is
6:15
here are you going to figure it out oh
6:17
GPS
6:18
gps
6:21
because without a
6:24
GPS there
6:29
every single one of you guys has used a
6:31
GPS before yeah when I'm in a different
6:34
state when I'm here I don't need GPS it
6:37
was not for my liking thank God for GPS
6:42
trying to ride you don't drive you're
6:43
like "Yeah but she doesn't know where
6:46
she's going." How many words per minute
6:49
are you able enough i've heard enough
6:52
for you a little bickering so now I'm
6:53
going to get to my lesson right so now I
6:55
want to find the distance between A and
6:58
B giving the coordinates so my job is to
7:01
put a label on top of them right i'm
7:03
going to call a
7:05
X1 Y1 and B is going to be X2 Y2 now let
7:09
me ask you a question does it matter
7:11
whether I label A X1 Y1 or B X2 Y does
7:14
it matter no no if I label B X1 Y1 then
7:17
I can label A X1 X2 Y2 so B I just want
7:21
to make sure you understand that it
7:23
doesn't matter how you label them but it
7:24
does matter how you apply the formula
7:26
right so that matters so now we're going
7:28
to put it in here right
7:31
so plus okay and I'm going to put it as
7:35
a square and I say square so
7:37
here it's going to be x1 - x2 right x1
7:41
is going to be what what's x1
7:45
x1 is -2 -2 minus x2 what's x2
7:53
y1 is
7:56
y2 is y2 is three there you go thank you
8:01
right and then we just got to plug it in
8:03
now right so now again you need to know
8:05
your basic
8:08
uh computations what's -2 -
8:11
4?6 -6 thank you very much what is 1 - 3
8:17
no2 -2 square right now I'm back here
8:21
now
8:23
what's -6 squar2 no what's -6 square 36
8:28
what is square 36 36 right what is -2
8:34
square um four
8:37
right
8:38
therefore this is what root of 40 and I
8:41
can plug that in my calculator if I want
8:43
or I can leave it as a square root of 40
8:45
right now the question is this am I
8:47
going to have plus or minus or just one
8:49
answer here
8:51
distance can't be negative the distance
8:53
cannot be negative so it's it's only
8:55
going to be a positive right if you plug
8:56
it in your calculator you can find what
8:58
it is and you can approximate it okay
9:00
now okay let's say the Jagger family is
9:05
visiting DC right the Jagger and that's
9:08
a family in the book the Jagger family
9:11
is visiting DC find the distance between
9:13
the Department of
9:15
Defense which is located at -29 and the
9:18
Madison building at 33 you guys go ahead
9:21
and try this and see how you can find
9:22
the distance between the Department of
9:24
Defense and then Madison building all
9:27
right I want you all to try to figure it
9:28
out using the distance formula tell me
9:31
how these are far far apart what's the
9:35
distance between
9:37
this is -29 and this is 33
9:47
of
9:50
defense
9:52
defense why does that look like what
10:04
defense your family defense that's what
10:06
it is
10:09
all right so now go ahead and figure out
10:11
what's the distance between Madison
10:13
building and the department of defense
10:18
you don't know what to do have to give
10:20
me a minute to do it mhm
10:29
we're doing the application of the
10:30
distance formula right i want to find it
10:33
the the distance between the two
10:34
buildings given that coordinates so I
10:37
want to figure it out right
10:44
excuse me
10:46
144 i'm walking calculator
10:52
did y'all know that what i'm a walking
10:54
calculator no you're not you're what
10:57
you're not what's 35 * 71 that was easy
11:02
okay solve it right now too late
11:06
you guys are making me laugh 35 times
11:08
what
11:10
[Laughter]
11:18
35 what stop
11:21
just saw me do I need to solve a square
11:23
root uh yes please
11:26
what's the square root that was the
11:28
easiest thing ever can I like punch in
11:30
2485 oh my god
11:34
2485 that's easy give me another one but
11:37
you need a second to calculate 100
11:40
105 no 111* 4 you're not a human you're
11:45
going to put your hands above the desk
11:47
i'm going to put your hands on the desk
11:50
look down that's so easy let me think
11:52
put your hands on your desk
11:56
5616
11:58
mr put your hands on your desk like this
12:12
779* 5
12:15
175
12:16
that's Yeah
12:20
I don't know why are you guys asking so
12:23
many questions what is
12:24
396id 15 that's easy
12:30
let me have that calculator i'll give it
12:32
to you in a minute
12:34
okay yeah that
12:41
you need a calculator all right i'm the
12:44
human calculator
12:48
mommy what is wrong with
12:50
nothing so what did you all get i got it
12:54
i got 13 13
12:58
i was trying to look i got 13 mr salami
13:01
13 good anybody got 13 i don't know
13:07
so
13:10
you um That's not positive 144 not 114
13:13
oh look that's not
13:20
comprehension skills i don't know i
13:23
don't even know how to do all right so
13:26
to do this right like I say
13:30
we're going to call this what x1 and
13:33
what y1 and we're going to call this
13:35
what x2 and Y2 right and we're just
13:38
going to apply the formula straight up
13:41
okay so the distance between the two
13:43
buildings is going to be on this
13:46
roo of -2 - 3 square right
13:49
plus of 9 minus -3 square now watch
13:53
this you have to be extremely careful
13:54
here your algebra has to be really on
13:57
point because we did this in the very
13:59
first in the beginning of our year right
14:01
so now we have the distance 144 not 114
14:05
yeah 144 so it's 55 square right plus
14:09
12 okay so this is
14:13
25 plus like I say 144 and this is of
14:17
169 which is basically 13 so between the
14:21
department of defense it's about 13
14:23
miles okay 13 miles so now you know it's
14:26
13 miles okay now let me ask you a
14:29
question let's say we have this
14:33
uh triangle here right i'm going to ask
14:35
you a question and I want you to find
14:37
the perimeter of this triangle i want
14:39
you to find the perimeter would that be
14:41
five uh5 yes this is five
14:46
so we just have to add all that
14:49
add all that
14:50
no so how would you find the perimeter
14:54
of this triangle i would add you got to
14:57
do X the distance between A and C C and
15:02
B and B and A now let me ask you a
15:04
question what would be the easier way to
15:06
do it find a a c and b and then how
15:09
would you find the distance between a
15:10
and b you can apply what the distance
15:12
from here yes you can apply that or you
15:14
can apply
15:16
pyagorean theorem right so you have
15:18
multiple options here so I want to find
15:20
the perimeter of this triangle first I
15:22
want to find the distance between a and
15:24
c i also want to find the distance
15:26
between what b and c and I want to find
15:29
the distance between a and b and then at
15:30
the end I'm going to do what i'm going
15:32
to add them all together so go ahead and
15:34
find for me and that's going to close
15:36
down
15:37
the distance between what so you what's
15:40
how do you find a perimeter you add all
15:43
the sides
15:45
add to find the distance between A and C
15:48
and A and B and C right how do you do
15:50
that how do you find the between A and
15:53
C formula you got to use the formula
15:56
right and then find the difference
15:57
between B and C we're going to use the
15:58
formula and then the same thing here and
16:00
then we just add for a while arithmetic
16:03
together right so basically this is his
16:05
chapter all right