Learn XY Coordinate Plane, Graphing Points, Lines & Distance - [5-9-15] - Free Educational videos for Students in K-12

Learn XY Coordinate Plane, Graphing Points, Lines & Distance - [5-9-15] - By Math and Science

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00:0-1	Hello . Welcome back . The title of this lesson
00:02	is called distance on the coordinate plain . This is
00:05	part one in this lesson . We're going to use
00:08	the skills that we have learned before . We're going
00:10	to be plotting points on the coordinate plain . And
00:12	then we'll ask a question about what we have drawn
00:15	and we can then see that by plotting points on
00:18	a plane we can actually solve real math problems .
00:21	So let's take a look at our first problem here
00:24	. We have our coordinate plane as we always have
00:26	here . And we have the question , A line
00:28	runs from two comma 3 to 8 comma three .
00:31	How long is the line now ? If you don't
00:34	draw a graph of this , it's very hard for
00:37	us to just look at that and say I know
00:38	how long that line is but by plotting it we
00:41	can see what we're trying to do here . The
00:43	first point is two comma three . Two comma three
00:48	. So how do we plot that ? X is
00:50	to y is three , so we go to X
00:52	two and Y is 123 Always X comma Y remember
00:57	too is first and three a second . So it's
00:59	two comma three and there is one end of the
01:01	line . Next eight comma three is the end point
01:05	of the line , X is eight . So we
01:07	go to X is equal to eight and then we
01:09	go up three units for why 123 Y is equal
01:13	to three and X is equal to eight . And
01:16	here is the end point of the line . So
01:19	we have now two points of the line . So
01:21	the line runs from this point to this point .
01:23	We have now drawn those points and now what we
01:25	want to do is actually draw a line between these
01:29	points . Now I could just freehand it but let's
01:31	make a little bit neater and try to draw this
01:34	line as straight as we can from the endpoint .
01:37	So now we've drawn kind of a line segment that
01:39	starts at this point and it terminates over here .
01:42	Now the question isn't really asking us just graph the
01:45	thing , the question is , how long is the
01:48	line ? So you might think about this in terms
01:51	instead of just thinking of it as coordinates , think
01:53	of it as city blocks . Right , this is
01:55	one block , two blocks , three blocks . Or
01:57	you can think of the X axis being in feet
01:59	, or the X axis being in meters . So
02:02	this is the end point at two m comma three
02:05	m from the origin from the origin , meaning the
02:08	corner here And then the other end point is eight
02:11	m away , And then three m up . So
02:14	what is the length of this line in meters ?
02:15	Well , I just need to count how many meters
02:18	uh , along the line is . So starting from
02:20	the starting point , we just count 123456 And the
02:27	answer to this is the line is six units long
02:30	. So the distance I'll put here , the length
02:33	of this line is what ? Six ? Now ,
02:37	I didn't put meters or kilometers or anything because the
02:40	problem doesn't tell me what units I'm working at .
02:43	But the point isn't really the units . The point
02:45	is to understand what you're doing . If you're representing
02:48	maybe you're planning a city , right ? And you're
02:50	trying to figure out where the buildings are going to
02:52	be in the city , then maybe your your coordinate
02:57	system . The numbers might be measuring kilometers . So
03:01	if this is the City hall , the center of
03:03	the city , let's say , then maybe two kilometers
03:06	to the right east , and then three kilometers up
03:09	from City Hall , which is the starting point ,
03:11	That would be maybe the fire station , maybe that's
03:13	what this point is . And then maybe the schoolhouse
03:17	is way over here from city , from the center
03:19	of the city , eight kilometers this way , and
03:21	three kilometers up . So the two end points might
03:24	be measured in kilometres from the city center . Right
03:28	now , we have a straight line between the fire
03:31	station , I think , I said , and and
03:33	maybe a school . How many kilometers is it from
03:36	the starting point to the ending point ? From the
03:38	fire station to the school ? Well , we can
03:40	just count because we know if these are measured in
03:42	kilometers and these are measured in kilometers , then the
03:45	distance along the line will be in kilometers because that's
03:47	one kilometer , one more , one more , so
03:50	123456 kilometers . Now , I could put kilometers here
03:55	, but the problem doesn't tell us . I'm just
03:57	giving you an example of what it is really .
03:59	It's six distance units along that line . That's the
04:02	whole point . All right . So , we use
04:04	grids like this to represent locations on Earth for maps
04:10	. You know , you might look at a map
04:12	or a globe and you might look at longitude and
04:14	latitude . That is a different kind of coordinate system
04:16	. But it's the same idea . You have to
04:18	go one direction than the other direction to find a
04:20	point on the map . And then the distance between
04:23	the points you can then measure by using , you
04:26	know , actually measuring it . A straight line distance
04:28	. Problem number two , it says a line runs
04:31	from this point to this point . How long is
04:33	the line ? Same story . So let's plot the
04:35	points of the line . Five comma nine x is
04:38	five right here . X . Is five . And
04:41	then why is 9123456789 The point would be Right here
04:47	at this intersection . five for X . And nine
04:50	for why ? 2nd 0.5 comma 15 is here for
04:55	X . Don't forget excess first . And then why
04:57	is one ? We just go up one unit .
04:59	So it would be right here . That would be
05:01	the end point of that line there . All right
05:05	now , just to make it neat . Let's go
05:07	ahead and just connect these guys who can see what
05:09	we're dealing with here . And the line would look
05:12	something like this . So the question says , how
05:15	long is the line ? Another way of asking that
05:18	is what is the distance between these points along that
05:21	line ? So the distance or the length of that
05:25	line ? Same thing is what we just start from
05:27	one end point and count . One unit , 23
05:30	45678 distance units . The distance is eight distance units
05:37	. Right ? And of course you can count going
05:40	this way or you can count this way , we
05:41	can go up 12345678 distance units . Now again ,
05:46	we could have the city centre be right here at
05:50	the 00 point of the coordinates , and then this
05:53	might be representing my home five kilometers east and one
05:57	kilometre up . That's my house Relative to the center
06:00	of the city . And then maybe my work is
06:02	up here far five km east and then nine km
06:06	up . That could be my work . So my
06:08	question would be then , how far is it from
06:11	my home to my work ? So I just count
06:13	, and if all of this is in kilometers ,
06:15	it's 1 km2 km , 345678 km away . That's
06:20	just one example . It could be representing lots of
06:23	different things , but that is what we use coordinate
06:25	systems for to measure things . That's what we actually
06:28	find it useful for . Alright , problem number three
06:32	. It says a rectangle has points . Uh ,
06:37	one comma 51 comma 17 common 17 comma five .
06:40	What is the perimeter ? That's what this means .
06:42	Perimeter equals question mark . Remember perimeter is the distance
06:47	. All the way around the object . You just
06:49	add up the distance of all the sides . So
06:51	first we have to plot these points and see what
06:53	kind of shape it makes . Rectangle says one comma
06:57	five X comma Y X is 15 is 12345 for
07:03	why ? So it's one for X . Five for
07:05	Y . So here is one corner of the rectangle
07:08	. All right , Next one comma one , X
07:11	. Is one , Y . Is also one .
07:14	So you go X . One and Y . One
07:16	next we have seven comma one that means seven for
07:19	X . And one for why ? So that means
07:22	the next corner of the rectangle is here . You
07:24	can probably guess where the final corner is . Seven
07:27	, comma five , X . Is equal to seven
07:29	and Y is equal to five . So the final
07:32	corner is right here . Now , what does this
07:35	thing look like ? You can already kind of see
07:36	, But let's just be , you know , let's
07:39	just be as as clean as we can . So
07:40	we can really understand everything . Will draw those two
07:43	sides like this and then we will draw the final
07:47	two sides that can line it up correctly like this
07:51	. And of course it forms a rectangle . So
07:54	you might think maybe you're planning a city and maybe
07:58	the maybe this rectangular region is representing the city park
08:04	in the center of the park . Central Park ,
08:05	let's say it's a rectangle . All right , so
08:07	what you do is you say this is the center
08:09	of the city , and one corner is one kilometer
08:12	over and one kilometers up . The other corner is
08:14	this one . The other corner is seven kilometers And
08:17	one up and seven km and five up . And
08:19	this makes a rectangle . What is the perimeter of
08:22	that park ? How many kilometers all the way around
08:25	that park ? How do we figure it out ?
08:26	We have to add the distances up . What is
08:29	the distance from here to here ? We just count
08:32	one distance unit , 234 distance units . So we
08:35	have a four here . What is the distance unit
08:38	over here ? It's also for 1234 So we have
08:41	a four plus a four . What is the distance
08:44	unit from here ? Going over 123456 And this distance
08:49	is the same thing . 123456 So what we have
08:53	to do is we have to add these up .
08:56	Now I know that six and 4 make 10 and
08:59	I know that this six and four also make 10
09:02	. So without even doing much , I know that
09:03	I have 10 plus 10 . It's gonna be 20
09:06	. So it's going to be a parameter equal 20
09:12	. Now , 20 . What ? Well , it
09:13	depends . What are you measuring it ? If you're
09:15	measuring a gigantic city park in all of these distance
09:19	units are in kilometers , then the perimeter is 20
09:22	kilometers . If you're measuring maybe quilt you're making ,
09:26	then maybe this is in centimeters or maybe it's in
09:29	meters or something like maybe something like that . Then
09:31	the perimeter would be in the same units of meters
09:33	or whatever it is you're measuring . So here ,
09:35	I'm just gonna leave it as perimeter equal to 20
09:37	because I haven't really told you what the distance unit
09:39	is . All right . We have one more problem
09:41	. Let's conquer that one right now . Alright ,
09:45	here we have problem number four . We have a
09:47	rectangle with these points and we want to find the
09:49	perimeter . We're going to do the same exact process
09:51	we did last time . The 1st 40.3 comma nine
09:54	Xs three go up nine units for Why ? That
09:59	means one corner is right there . Next three comma
10:02	three , It means X is three and wise also
10:05	three . That means the point goes right here .
10:07	Three comma three . Four comma three means X is
10:10	four and y is three . So that means the
10:13	point is right here . Finally , we have four
10:17	common nine , X is four . Why is nine
10:20	? Why is nine ? That means the fourth corner
10:22	is right here . All right . And just for
10:25	neatness , we can try to draw this . So
10:28	we have one side of the rectangle , right there
10:31	. We have another side of the rectangle right there
10:34	. And then you can draw this side right here
10:37	and then we can draw this side right here .
10:39	So again , we could be making a bedspread or
10:41	quilt . This could be uh some kind of like
10:44	plot of land for farming . I mean , who
10:45	knows what it is ? But it makes a rectangular
10:47	region . What is the perimeter ? So we have
10:50	to add up the distance is what is the distance
10:52	between here and here ? It's only one distance unit
10:54	. So , there's a one here then . What
10:57	is the distance here ? Also one . All right
11:00	. Now , what is the distance between here and
11:01	here ? We just count 123456 That's six distance units
11:07	. The distance here is the same thing . 123456
11:11	units . Right ? Six plus six is 12 and
11:14	13 and 14 . So , what we get out
11:17	of that is 14 is equal to the perimeter .
11:20	Perfect . Yeah . Right . So let's say I
11:25	was making a garden and This is maybe like the
11:28	center of my house . The one corner of the
11:30	garden is three m away from my door and 3m
11:34	up . And then the other corners are all laid
11:37	out as I've said . But everything is in meters
11:39	. Then what we're figuring out is the distance all
11:41	the way around this thing would be 14 m .
11:43	That's what the perimeter is . If we're measuring something
11:46	smaller , like something you're like a craft and it's
11:48	in centimeters . then all of these distances will be
11:51	in centimeters in the perimeter will be 14 centimeters .
11:53	If you're measuring something in kilometers it will be in
11:55	kilometers and so on . So here we have conquered
11:59	the idea of finding distance using a coordinate system or
12:02	coordinate plane . We use the points that we have
12:04	now learned how to plot to mark locations on the
12:08	coordinate plain . And now we're starting to connect the
12:10	dots here with a line and then here we can
12:12	enclose shapes and start to ask mathematical questions like perimeter
12:17	. Later we'll be doing area and so on .
12:19	Related to those shapes here . I've kept it pretty
12:21	simple with rectangles but you can see how you can
12:24	make very intricate , detailed , complicated shapes and still
12:27	use the coordinate system to answer really important questions .
12:30	So it's a very important skill . Practice these yourself
12:33	. Follow me on to the next lesson will continue
12:36	conquering the topic and getting practice with distance on the
12:39	coordinate plain

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