i've organized my channel into playlists so you can go in order. check out the "featured playlists" section in the sidebar of my channel page, and start with limits & continuity. that should help get you going in the right direction! :)
you certainly don't have to for this particular problem, but using integrals to find the area of shapes like this can be really helpful when the shape is more complex (like a polygon). so it's a good skill to have! :D
Krista. You're gonna laugh, but I found a cute little trick that always works. If you pick a vertex on a plotted triangle, and form the two vectors that connects it, and then you cross product them, you will get an orthogonal vector. If you take the magnitude of it, then that will be the area of a parallelogram. If you take half of that value, then that will be the area of a triangle. Yes, you can do it with calculus too, but the vector way is a lot faster and it always works. LOL
Hi Krista King Loved your tutorial just gonna ask what about finding the area of the triangle formed by joining coordinates A(2,2),B(4,10),C(11,2)D(9,7) FOUR VERTICES. hope of recieving ur reply asap. Hahaha thank u
WOW! I could've swore that you're either a teacher or a college professor. You are so astute. If you don't mind, I must ask, what's your major? Are you employed in that field?
Yep. Just did it. Put 3i + j + 0k and -2i +j+0k in a determinant, use Cramer's rule. You get 5k. Take the magnitude of it you get 5. 5 is the area of the completed parallelogram. Now take half of that to get the area of the triangle. BINGO! You get 5/2.
This code from stack overflow tells me I can do it using cross product. stackoverflow.com/questions/11262391/from-barycentric-to-cartesian double triArea = (p1 - p0).cross(p2 - p0).norm() * 0.5; I am looking for a youtube explanation that does it this way. As it looks pretty elegant.
Isn't a triangle just a 1/2 of a square, rectangular, rhombi or a parallelogram, WHY THIS MUCH COMPLICATION ??, I would get the answer in a fraction of the time, AND EVERYONE WOULD UNDERSTAND, I'm dumbfounded I do not get it, sorry but anyway, thank you for the video.
or you could just use the area of a triangle bh(1/2) and add the two triangels smaller triangle area=1 bigger triangle area =1.5 1+1.5 =2.5 =5/2. Done. :3
Oh my goodness, thak you so much, I was struggling trying to find an explanation to this exact topic, for my calc II course. You have truly saved my day, again thank you
Is this elements of calculus, or calculus? Because this seems very difficult and I'm supposed to take elements of calculus in order to graduate. I don't remember this in algebra (i took it about 5 years ago).
Eight years later and this is still helping people. Stewart's online help videos that come with the online homework are garbage, I went from being confused for 45 minutes to understanding 6 minutes into your video. Thank you.
the coordinates of three vertices (corner pionts) of a rectangle are( -4,3) (5,3) and (5,-2) Plot the fourth vertex of the rectangle on the Coordinate plane grid. Help ... put more out there thanks ,is there an easy way?
perfect explaning . I really forgot these calculus but your explanation wonderful so remembered now thanks friend. are you a teacher? otherwise you should be :) greetings from turkey
by the way. I want to repeat calculus from here so which video I must watch first in your channel ? because there are many videos. can you make a list that subject's arrange? thank you
It is because Krista wants to teach you how to apply calculus to solve this problem. Although this problem is simple, it is not a bad thing to know more methods to do solve this problem. Besides, the determinant formula can be derived using calculus.
![[UNCUT] “บอสณวัฒน์” ลากไส้!! ใครหนุนหลัง "แม่ตั๊ก ป๋าเบียร์" I คนดังนั่งเคลียร์ I 30 ก.ย. 67](http://i.ytimg.com/vi/QlD7mU2KKRk/mqdefault.jpg)
i've organized my channel into playlists so you can go in order. check out the "featured playlists" section in the sidebar of my channel page, and start with limits & continuity. that should help get you going in the right direction! :)
you certainly don't have to for this particular problem, but using integrals to find the area of shapes like this can be really helpful when the shape is more complex (like a polygon). so it's a good skill to have! :D
hey elizabeth! just plot those other three points, and you'll be able to see the fourth one emerge easily. hint, it's (-4,-2). :)
Who's here rn alot changed u uploaded this vid when i was 5 yr old lol😂😂
yep! the answer is 5/2 units^2. :)
Krista. You're gonna laugh, but I found a cute little trick that always works. If you pick a vertex on a plotted triangle, and form the two vectors that connects it, and then you cross product them, you will get an orthogonal vector. If you take the magnitude of it, then that will be the area of a parallelogram. If you take half of that value, then that will be the area of a triangle. Yes, you can do it with calculus too, but the vector way is a lot faster and it always works. LOL
so complex why would you use integral??
I don't understand this.
I find you very useful for me !! every time that i have problem i always come back to your youtube chancel keep up the good work :)
i'm only a teacher on TH-cam, but that makes me feel like a teacher!! :)
Hi Krista King Loved your tutorial just gonna ask what about finding the area of the triangle formed by joining coordinates A(2,2),B(4,10),C(11,2)D(9,7) FOUR VERTICES. hope of recieving ur reply asap. Hahaha thank u
You should be a school teacher. You're very smart. I am a teacher.
WOW! I could've swore that you're either a teacher or a college professor. You are so astute. If you don't mind, I must ask, what's your major? Are you employed in that field?
Glad I could help!
This is definitely the best explained video on this type of problem. Thank you! I was stuck for a bit.
Glad you liked it! Thanks for the comment. :)
You definitely need algebra before calculus. It would be really hard to understand otherwise.
Krista King and friends: How do you know where to draw the dividing line for more complex shapes.
Yep. Just did it. Put 3i + j + 0k and -2i +j+0k in a determinant, use Cramer's rule. You get 5k. Take the magnitude of it you get 5. 5 is the area of the completed parallelogram. Now take half of that to get the area of the triangle. BINGO! You get 5/2.
The expressions under the sign of integral (except dx) must be in parenthesis.
Aw thanks!
why are you subtracting once you get all 3 equations ?
This code from stack overflow tells me I can do it using cross product.
stackoverflow.com/questions/11262391/from-barycentric-to-cartesian
double triArea = (p1 - p0).cross(p2 - p0).norm() * 0.5;
I am looking for a youtube explanation that does it this way.
As it looks pretty elegant.
then what is your job? engineer may be? İ wish I would study calculus with you. My All respects.:)
Isn't a triangle just a 1/2 of a square, rectangular, rhombi or a parallelogram, WHY THIS MUCH COMPLICATION ??, I would get the answer in a fraction of the time, AND EVERYONE WOULD UNDERSTAND, I'm dumbfounded I do not get it, sorry but anyway, thank you for the video.
or you could just use the area of a triangle
bh(1/2) and add the two triangels
smaller triangle area=1
bigger triangle area =1.5
1+1.5
=2.5
=5/2.
Done. :3
Cihan Barnett The idea is to use calculus, which requires integrating.
Thanks a lot, very helpful.
Oh my goodness, thak you so much, I was struggling trying to find an explanation to this exact topic, for my calc II course. You have truly saved my day, again thank you
i understood nothing well maybe i need to take algebra I and 2 first??
Thank You soooo much. Really helpful. =D
great video
This video is awesome. The solving process was very well explained. Thank you and keep up the good work!
can you do an example where part of graph of the triangle is below the x-axis? How would that be computed?
PHILIPPINES, THE COUNTRY WITH THE SLOWEST INTERNET CONNECTION. JUST TO SHARE!
dew vhaxilyu Well, it's your problem not ours. Besides, sharing it with us wouldn't help solve it, would it?
This is so confusing,??? But I wrote all of it down any way because I'm learning about area in triangles and parallegrams
Thanks, you helped some of us ey :)
I found out what I was getting wrong was not putting the small negative at 5x2/12 after integrating it
Is this elements of calculus, or calculus? Because this seems very difficult and I'm supposed to take elements of calculus in order to graduate. I don't remember this in algebra (i took it about 5 years ago).
This is integral calculus.
Can you help me with this coordinate (0,20),(5,0),(20,15)
Eight years later and this is still helping people. Stewart's online help videos that come with the online homework are garbage, I went from being confused for 45 minutes to understanding 6 minutes into your video. Thank you.
I'm so glad this helped clarify. Thanks for letting me know, Autumn! :D
the coordinates of three vertices (corner pionts) of a rectangle are( -4,3) (5,3) and (5,-2)
Plot the fourth vertex of the rectangle on the Coordinate plane grid.
Help ... put more out there thanks ,is there an easy way?
I'm revisiting this after 11 years since being in a classroom and I understood your example. A heartfelt thanks from some guy in Canada :-)
+truerthanyouknow It's never easy after having such a long break. Glad I could help!
Ads are so annoying gosh
perfect explaning . I really forgot these calculus but your explanation wonderful so remembered now thanks friend. are you a teacher? otherwise you should be :) greetings from turkey
by the way. I want to repeat calculus from here so which video I must watch first in your channel ? because there are many videos. can you make a list that subject's arrange? thank you
an easier way is to look at the length of line x=1 between y=(1/3) x and the point (1,2), which is 5/3, then the area = .5 * (5/3) * 3
tyvm sister in humanity :) idk how to thx u :/ i wish u'll have a super great job that u like :D
+lounis nei thank you!
Can somebody explain me how did she get 5/2 in the second equation ? please ASAP
+carl tua if you look at the graph on the left, it's from the equation of the line that connects (1,2) to (3,1).
you are just doing the questions we need and your explanation is sooo gooooood 😉😉😉😃😘😘
Thanks! I'm so glad it helped! :D
Great man.
first!!... to learn area of the triangle with the given vertices.
Love uhh
Since its area would we add square units to the final answer?
Look up the Shoelace formula, its so easy
congratulations
is there any other method other than integral?
Well done. Super Clear. Love it. Thanks!
Much thanks m'am
You're welcome, der! :)
Thanks for the help!!!!!!!!!!
Thanks very helpful
i didnt get a heck
Thank you SO much, that was very helpful!
Thank youuuu!!!
You're welcome, Tourushi! :D
God bless you.
2.5
your voice is hot, i'm learning lol :D
perfecto :p
Thank you for this ❤️
You're so welcome, Glenn! :)
Thank you very much
You're welcome!
Thank you!
You're welcome, Diana! :D
but in my gcse book it is quadrilaterals not even triangle
lol u can split it into two triangles and do it if u rlly want
uuhhmm slow down a bit lol..,. besides that thanks for the help ;)
Why not solve this through determinants? Easier to understand and much easier to perform.
I was just trying to explain this particular method, even though it might not be the fastest way. 👍
Y TO DO SUCH A LONG DAMN THING,WHEN WE KNOW THE SIMPLE DETERMINANT FORMULA?
It is because Krista wants to teach you how to apply calculus to solve this problem. Although this problem is simple, it is not a bad thing to know more methods to do solve this problem. Besides, the determinant formula can be derived using calculus.
Some problems require you to solve it using integral.