Find the Equation of an Altitude in Triangle

[@___Vortex___]

I love how you miss one day of AP Math and you suddenly missed everything!!! Thanks for helping me catch back up!

[@aahahafightme9183]

Honestly I missed one lesson and I had no clue what the homework was going on about lol

[@dionysis8906]

@@aahahafightme9183 bro we doing this in 9th grade 😭😭😭

[@baldibaldimore6423]

@@dionysis8906 2 years later, WE STILL DOING THIS IN 9TH GRADE LMAO

[@lucasfiniello8290]

those views just show how many people are struggling with math

[@djnechodom]

I agree, Lucas, and I'm excited about that. Not that I get excited that people don't understand, but I do get excited about having people willing to struggle, and to put in effort to find resources to gain understanding.

[@woolyoshi1154]

Lucas Finiello tbh: math is my worst subject in school

[@meganhu373]

@@djnechodom Thanks for the video I have been struggling with math and I have a test coming up. You have explained everything I need to know. Thanks!!

[@matthewgaray2859]

Stop exposing me lol

[@julianplayzgames]

@@djnechodom Poggers dude

[@vnumber100]

THIS WAS SO HELPFUL AND HE WAS SO FRIENDLY AND CUTE I LOVE IT

[@HolidayParty173]

Thanks so much!! You're like that one rare math youtuber who actually teaches math well and makes it straight to the point. Thank you so much for helping

[@djnechodom]

I'm so glad I could help. I'm blessed to be able to hone my craft and share the results.

[@blasp0]

Studying for my exam, this really helped me study. thank you :)

[@Rerlio]

This was so helpful and clear! I have a test tomorrow and this helped me soo much!

[@bambiii787]

How was that test

[@MrScottishBloke]

YOU GENIUS. I love how maths is universal, cheers mate!

[@DevyGamesProductions]

holy crap dude. I've searched for over an hour for a good explanation for this because I've forgotten it from math class. you've just made my math project so much easier! Thanks!

[@dh6414]

you totally saved me, you're the reason I didn't get this wrong on a test so bless your soul

[@djnechodom]

I'm so glad I can help, even 11 years after it was posted. And, yes, my soul is blessed.

[@cr33py95]

THIS HELPED ME SOOOOOO MUCH

[@djnechodom]

So glad to hear it!

[@whosjoe1082]

If the slope is positive would flipping it over make it negative?

[@djnechodom]

If you were in my class, I'd smile reassuringly and say, "No, but I see what you mean, so yes." Flipping it over doesn't make it negative it just finds the reciprocal. But you want the opposite reciprocal, so yes, after you flip it over, make it negative. Clarifying (hopefully): perpendicular lines have slopes that are opposite reciprocals. One is positive, the other is negative and 'flipped over.'

[@EuphoriaxCanada]

Thanks a lot for uploading these videos. I finally get it now

[@Aman-lm1ky]

You made me understand it much clearer than my teacher taught me , Thank you.

[@djnechodom]

Ashlea Camarra, I couldn't reply back directly to your question, so I hope you see this. I don't have the time to create a video at the moment, but I want to at least give you something to go on. For that triangle, you're going to be doing the same thing as in the video. If it helps, put the points on a graph, and notice you have to go down and right along the line AC to get to R, where CR would be perpendicular to AC. Then do what we did before: Find the slope of AC, then get its opposite reciprocal, which is the slope of AC. Use that slope, and B, to get the equation of the line BR. If that doesn't make sense, email me at school at dann(at)daytonsd.org and I'll try to be more clear.

[@woolyoshi1154]

Oh my gosh, I can't thank you enough for this video. I was literally getting so upset because I couldn't figure out altitudes and when I saw your video it immediately made sense to me. Thank you so much, you are a life saver 😀😄👍🏻

[@jimmybarraza9384]

When this was posted i was doing simple multiplication now 9 years later im here thats crazy

[@kajanrajamohan3124]

Thanks for the help man, my teacher can not teach at all but you are one hell of teacher. Got yourself a new subscriber.

[@WestCoastLefty]

You just saved my geo honors final grade

[@djnechodom]

Wow! I'm honored to have been able to help. Best to you.

[@djnechodom]

LOL. I may or may not find $20 on the ground, but knowing I was able to help is a very good reward. Good luck. Dan

[@AlyssaSasser-sr8ke]

This was extremely helpful. Thank you so much!!

[@djnechodom]

I'm glad the videos were helpful. I know they're old, and they're not very fancy, but I find that some people just want to have things explained to them simply. Best to you.

[@evad.8453]

The problem I'm doing is on an obtuse isosceles triangle. It doesn't give me the points, only the length of one side (the base) which is 10. How do I solve that problem?

[@djnechodom]

Eva, If they only gave you the length of one side, then you can't get the equation. There needs to be some information about the location of one of the points, or perhaps some angles. If you'd like, you can snap a picture of the problem and sent it to me at dann (at) daytonsd (dot) org. I'll be happy to help.

[@josefferd5]

You just made my life in honors algebra 2 so much easier. Thank you so much, keep up the good thorough work

[@djnechodom]

Yihao, I'm happy to help you, but I need more information. If all you were given about side AB was the coordinates of A and B, or maybe just it's length, then you can't answer. Is there any other information given?

[@ChildTerminator]

bit late, but this is the only video that explained it to me well. Its been 13 years since this was posted and I couldn't find a better explanation. Definitely better than my teacher and tutor.

[@djnechodom]

Glad it was helpful. I'm still teaching (32nd year) and still trying to help people make sense of this stuff.

[@two_boys_and_a_camera]

Thanks so much. Great video!

[@TheRealWiLDFiRE000]

If the question states, ' Find the equation of the altitude CP', which midpoint would we try to find?

[@djnechodom]

Ryan, if you're asked to find the equation of an altitude CP in a triangle with vertices A, B and C, then you'd be looking for the equation of a line through C to a point on AB. That line has to hit AB at a 90 degree angle. So it will likely not be the midpoint at all. (That would only happen if triangle ABC is isosceles with AC and AB being congruent.) If you're finding an altitude, then use the technique I showed in this video. If you truly need to find a line from C to the midpoint on AB, then I have a video that shows that as well. (Find the Equation of a Median in Triangle) Hope that helps.

[@epiclyfaled]

Thank you so much! I'm ready for my math test now!

[@dani.hana97]

u r amazing. didnt get it in class and have an assignment due tomorrow!!! but i totaly get it now:)

[@walesaje]

Thank you very much! Doing very important math homework. Like for you

[@danielxu5000]

Thanks man!

[@djnechodom]

My pleasure

[@hussein987123645]

Thank u so much man! This helped a lot! 😘😘😘

[@snaworld209]

You have saved my life!!! I have an exam tomorrow and i completely anm blanking on how to find the equation

[@dahe1352]

Thank you so much...I think I'm going to cry tears of happiness

[@djnechodom]

Thank you, I think. Last time I checked I wasn't 'god damned.'

[@djnechodom]

How can I help, Clarita?

[@ashleamarie]

Thank you for explaining this! I understand it so much better now! Would you be able to explain how you would find the equation of an altitude that was outside the triangle? I have an assignment where I need to find the equation of the altitude but it is outside an obtuse triangle. The points are A(-2,10), B(2,-4) and C(4,6) and I have to find the altitude equation of altitude BR. Could you please help me understand how to do this? Thank you so much!

[@Kar76060]

Thank you very much mate! Your amazing! :D - Subscribed

[@enochjayakody9769]

THANK YOU SOOOO MUCH!!!!!

[@karth.sarv22]

Thank you soo much!!

[@inoahmann7542]

Great video, thanks for the help!

[@shayanbaig5531]

Hello Sir. I was wondering, why wouldn’t you find the mid point of BC and then find the slope A to the midpoint of BC.

[@djnechodom]

I'm so sorry I didn't see this earlier. I hope you got your question answered in some way. I would find the midpoint of BC if I was finding the equation for a 'median,' which goes from a vertex to the midpoint of the opposite side. Since I'm find an 'altitude,' which intersects the opposite side at a right angle, then the midpoint isn't relevant. Best to you.

[@ariabrusch4132]

Really helpful! Thanks for makng the video!

[@noveled_1]

OMG THANK YOU SO MUCH I GOT A 100 IN MY TEST BCS OF YOU SIR YOU ARE AMAZING AHGEPOHEH

[@DaffyYT]

I needed this!

[@ajnuttela6594]

Thanks a lot you helped me

[@vickyyadav618]

Nice explanation Thank you

[@etangbose4755]

My teacher assigned hw on shit he didnt explain

[@djnechodom]

Bummer. Hope video helps. Comment back if I can help.

[@etangbose4755]

Dan Nechodom this helped and he taught it todau

[@lizboyer13]

Thanks this really helped!!

[@kasondemulenga3472]

Thanks so much, helped a lot!

[@roberttorres6693]

Thank you that was very helpful and informative!

[@VigilanceTech]

How do I now find the length of the altitude line?

[@djnechodom]

Kevin, I'm going to make the assumption that you either know how to find the hypotenuse (long side) of a right triangle, or that you're going to go watch a video on it. If you have that skill (finding the long side of a right triangle given the two short sides), then you're ready to go with finding the distance between the vertex and the point you found on the opposite side. For this part, you could look up a video for 'finding the distance between two points' or the 'Pythagorean Distance Formula.' Here's the basic idea: Draw a vertical line through one of the points, and a horizontal line through the other. You'll notice that these two lines, plus the altitude, make a right triangle. You can get the length of the horizontal side by subtracting the x-coordinates of two points. You can get the length of the vertical side by subtracting the y-coordinates. Now you have the lengths of the two short sides of the triangle, and you can find the length of the long side (the altitude) using the Pythagorean Theorem. Hope that helps.

[@vasilitalopez3267]

Thanks... Loved the explanation :)

[@djnechodom]

Glad I can help.

[@sonanegi1]

thanks man it helped

[@nicholasdidier4188]

That was helpful ,Thanks test tomorrow

[@Tranzendentall]

This was very helpful!

[@jamesjeffery1686]

Thanks, super helpful vid.

[@slimeball4l540]

Thank you idk why I'm so bad at geometry this helps more than my teacher

[@LynAlecciaDinh]

THANKS SO MUCH!

[@davewhite6288]

Wow thanks man

[@awak6n]

goated

[@aliciaadams2486]

your from brampton fam?

[@awak6n]

@@aliciaadams2486 nope from Toronto wbu

[@aliciaadams2486]

@@awak6n im from brampton llool

[@Thespiella]

thank you so much!! :)

[@AlexG-oo8kt]

GOD BLESS YOU. THANK THE LORD.

[@jenniferyin7468]

How do you do this with an obtuse triangle?

[@djnechodom]

Hi Jennifer. I'm assuming that you're talking about a triangle where the obtuse angle is NOT the one with the altitude going through it. But it will work the same way. Find the slope of the line through the two points that form the opposite side of the triangle, then find its opposite reciprocal. That will be the slope of the line you're looking for. Then you'll finish out the problem the same way. Good luck.

[@jenniferyin7468]

Thank you so much! Loved the video by the way :)

[@bambiii787]

Wait but how do you find the x value ?

[@djnechodom]

I'm really sorry. I don't understand your question. Happy to help if I can. If it helps, rewatch the video and tell me the time in the video for the part that doesn't make sense and I'll try to help from there.

[@aymanhaque1646]

thx 4 the help

[@casperlee302]

This was confusing at first but I’ve rewatched it and I think I get it

[@djnechodom]

If I can help, put your question in the comments and I'll try to respond quickly.

[@FU310N]

thanks so much

[@lauralucas9300]

How come for point BC you didnt use the formula y2-y1/x2-x1? You did y1-y2/x1-x2 which is 6(y1)- (-2) (y2)/ 6(x1)-8(x2)

[@djnechodom]

I would have gotten the same result either way. I just need to have the difference in y coordinates divided by the difference in x-coordinates. So I had no preference.

[@lauralucas9300]

Okay thanks so much. This video was very helpful btw

[@fraserallison29]

So do you not find the mid point for altitude ?

[@djnechodom]

Excellent question. You would find the midpoint if you were finding a median, since a median goes through a vertex and the midpoint of the opposite side. But altitudes go through the vertex and are perpendicular to the opposite side. So no need for midpoints. You'll need a point and slope to get the equation. You've got the vertex for the point, but you'll have to get the slope by finding the slope of the opposite side, the finding its opposite reciprocal to get the slope of the altitude (since they are perpendicular). Then you're ready to find the equation. (Side note: If the triangle happened to be isosceles, and you were finding the altitude through the vertex connecting the two congruent sides, then you could find the midpoint and make it work, since the altitude and median would be the same line. Be careful though, your teacher might want you to prove that claim before you use it.) Good luck.

[@fraserallison29]

@@djnechodom thank you that was really helpful

[@djnechodom]

@@fraserallison29 My pleasure. I got moved to teaching PE, after 28 years of math and I really miss it. Thanks for asking so I could help.

[@commanderoftheenhancementation]

this was very helpful

[@akeinaponsu]

Life saver!

[@sonictimm]

Thanks!

[@mariaangelasanpedro9892]

Hi sir :)... I'm just curious to ask something... How if for example, the slope of line BC = 0? Is the slope of the altitude undefined? Do I still need to find the altitude's equation if that happens? And what is the intersection point of the altitude's equations?

[@DanNechodom]

+Maria Angela San Pedro Great questions, Maria! I'll address them one at a time. 1) Yes, if the slope of BC is zero (ie it's horizontal), the the altitude through it is vertical, so it does have undefined slope. It's equation, if you need to find it, will be in the form x = #, where # is the x-coordinate of A. 2) If you need to find the intersection of the altitudes (the orthocenter), first, find the equations for two of the altitudes. (All three meet at a single point, but you only need two.) The video shows that the one through A is y = 1/4x + 2. The one through B is y = 3x - 12, which I found using the same method shown. Now you need to find the coordinates of the point where these two lines meet. To me, the easiest way is to recognize that since their left sides are equal to each other, then so are their right sides. So write this as an equation and solve: 1/4x + 2 = 3x - 12 14 = 11/4x (add 12 and subtract 1/4x from each side) 56/11 = x (divide by 11/4) Now substitute this value for x into either of the equations to find the y-coordinate. I'll use the first. y = 1/4(56/11) + 2 = 36/11. So the intersection is at (56/11 , 36/11).

[@mariaangelasanpedro9892]

Thanks sir! Such a great help! :)

[@jackhiggins9926]

thank you very helpfull

[@Rc2Go]

Upgrade from a potato, please...

[@djnechodom]

Jesse, please explain the potato reference. I can change and upgrade if I know what you mean.

[@Shcxir]

legend

[@kaushikreddy7992]

Thank you sir u saved me

[@emilymcausland1463]

OMG YOU JUST SAVED MY LIFE THANK THE LORD

[@DanNechodom]

That's good news. I'm glad I could help. Good luck with this stuff, it does make more sense as you work with it.

[@arjunkancharla9464]

this man almost helped SYKE

[@unofficialbeastx929]

Guys, he was just playing crab rave + ear rape in the background. Chill out.

[@djnechodom]

Probably not, actually. I made the video about 10 years ago. Even then, I was probably listening to Rush, Journey or KISS in the background!

[@abbystar111]

thanks

[@jimmyneutron9732]

Thank

[@arthurdelbeato1805]

this man is a fucking god

[@wolflordftw9528]

What if your only getting th side lengths

[@DanNechodom]

You'd need to know at the coordinates of at least one point. Can you post a description of the problem you're looking at? I'll see if I can help you.

[@brownieharrison6597]

I love you so much bro I wish u were my teacher

[@saadaziz1359]

Why did you do y1-y2/x1-x2 it's y2-y1/x2-x1 I'm pretty sure because I got a different answer which was y=-1/4+2

[@djnechodom]

If I subtract y1-y2, and you subtract y2-y1, we'll get numbers that the are the opposite of each other. Same with x1-x2 and x2-x1. If we each do a division, but your numbers are both the opposite of mine, shouldn't we get the same answer?

[@RedSquirrelHunter]

Thanks

[@lilloud116]

Isn't it supposed to be 8-6? Cuz it's x2-x1 ...

[@edwardb2804]

That is right if you intended for B to be the initial and C to be the second. But he switched them around, and I did the maths, its still right! 6--2/6-8=-4 and -2-6/8-6=-4. Good spot.

[@lilloud116]

Ohh okay nvm then

[@DanNechodom]

Thanks, Edward, for helping Mandeep out. That's the way math class ought to run! You're exactly right. It doesn't matter which way you decide to subtract, AS LONG AS you subtract the same direction on both of them. Mandeep, keep asking good questions, even if you end up feeling a little silly afterward. I'd rather have students (or employees) that ask questions to be sure they understand, rather than those who just keep quietly out of fear of looking wrong.

[@GeorgeDiVenere]

THANK YOUUUUUU!!!

[@danielnguyen6463]

thaank u

[@NeverSnooze]

haha thanks good tutorial

[@Hybrid-Equinoxx]

I fucking love you

[@ayannnh5422]

Bro bless this man he’s the reason I’m passing grade 10 math😂

[@DanNechodom]

I'm very happy to be able to help.

[@sohaibbaig248]

Lol can u be my teacher?

[@blurr1903]

Im here a decade too late but thanks lmao

[@djnechodom]

Never too late. Good luck.

[@blurr1903]

@@djnechodom yooo thanks brother hope it’s going good for you

[@Thethe0ryof]

Exam review, Its all coming back !!!

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ty my teacher taught me nothing

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i love you

[@djnechodom]

Well, you're very kind. I'm assuming that the video was helpful.

[@chopstickslover]

GOD, UR GOD