How to Find Orthocenter Given 3 Vertices (Algebraically)

Learn how to find the orthocenter algebraically given 3 vertices of a triangle in this math video tutorial by Mario's Math Tutoring. We discuss what the orthocenter is and how to find it. We make use of the slope equation as well as the point slope form of a line in this lesson to find the orthocenter.
0:16 What is the Orthocenter?
1:08 Find the slope and opposite reciprocal slope
2:00 Write the equation of the altitude using slope intercept form
2:24 Find the 2nd altitude using slope formula
2:52 Use point slope form of the line to find the equation of altitude
3:30 Use substitution to find the point of concurrency of the 2 lines
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[@spynix0718]

I normally do really well in math, but this topic stumped me, thanks for this video.

[@littlesimsfreak2931]

Same. Chapter 6 geometry has me dying

[@Dinoboy0217]

same

[@atharvavaishampayan5397]

Same my brother

[@bluedonkey180]

Thanks for bragging before thanking him (I’m really good at math and already know this i’m just here for fun)

[@andrewhaggar8011]

@@littlesimsfreak2931 im doing chapter 6 rn and I am struggling

[@pravithgouroji7721]

Watched the 1st minute and already learned more than I would in class.

[@videoclips9541]

Same here!

[@vahinnakkala1027]

ur the best tutor, whenever I don't pay attention in class I always come to u last min thanks

[@elandieugeorges1167]

same

[@wade9271]

what i just did

[@victorzhang6859]

@@wade9271 same lol

[@Anthony-pd9ur]

You teach better than my teacher

[@savagepotatoputato3643]

exactly what i do lmfao

[@samanthafeuer7100]

My teacher made this way harder than it actually is. You are such a good tutor. Thank you!

[@moosemaen]

My teacher is trash and horrible at teaching, this was so helpful, keep uploading great content and I hope your successful!!!

[@aadilshaikh4510]

This goes for like 95% of offline teacher

[@yani_tube]

Just what I was looking for!!

[@MariosMathTutoring]

Great!

[@Nico-yw2fi]

I’m good at learning math quickly, and since I almost never pay attention in class yk I gotta make a trip to this channel the day before a test

[@cadedvoid]

my test is in 30 min :)

[@jirahrobles3069]

Thanks a lot! I've been having a hard time finding the orthocenter using the way written in our modules. Following this step, I finally found it! You're such a great help! I'll subscribe. harts harts

[@harishanand1877]

Thank you mario. Really well explained. I have a test on this tomorrow, and this cleared everything up. Thanks a lot! Keep up the great work.!

[@MariosMathTutoring]

Best of luck!

[@rameshshrivastava]

Thanks love from India 🇮🇳

[@narendrasingh7504]

Your video is really helpful to understand this concept ...Love you from India

[@jenniferwagner580]

THANK YOU SO MUCH FOR EXPLAINING THIS SO WELL!

[@timothyfoley9222]

Excellent step by step video. Thanks

[@MariosMathTutoring]

Glad it was helpful!

[@ritzzzblitzz6833]

Oh! you made it much easier. Thank you so much!!!!!

[@mohamedyassin1212]

can i give you an equation to solve that equation is too easy compared with my one

[@LitFam309]

Thanks for the help

[@NepalLearning-br4hp]

Thank u and love from 🇳🇵 ❤❤❤❤

[@juliosica2098]

Thank you soooo much

[@enbaoliang6938]

wow helped me a ton

[@harishanand1877]

i love the sound of the whiteboard

[@anaelbrodski5117]

because of u i might not fail geometry thank you

[@rebeccashuster3373]

mario be going sonic speed. (but thanks, i really needed this)

[@gio4719]

lmao bruhh 😂

[@rebeccashuster3373]

@Piyush Meena hi?

[@rebeccashuster3373]

@Piyush Meena english...

[@rebeccashuster3373]

@Piyush Meena no :}

[@Alfredo5883]

Great! Thank u. Can u do a video on Limits?

[@MariosMathTutoring]

Finding Limits Precalculus Methods kzbin.info/www/bejne/pmGTl5-Kfa6hjpo

[@MariosMathTutoring]

Finding Limits Given a Graph kzbin.info/www/bejne/n3Syk32ZarFrgq8

[@Alfredo5883]

Thank you very much!

[@mangesh2347]

Thank you sir love you from india

[@lilida14]

I’ve been completely stuck on this and my teacher doesn’t really do a step by step(assumes we know alr since it’s honors geometry), but I needed this AND I LIT JS SOLVED THIS QUESTION IVE BEEN STUCK ON FOR DAYS!! THANK YOU SM

[@MariosMathTutoring]

Happy to help!

[@DesiredSlayz]

Are u prepared for chapter 5 test tomorrow/friday lmao

[@baileyradel3104]

Soooo clear! Thanks, man.

[@askme5271]

wooow this helped me ....thank you for your wonderful marvelous amazing beautiful adorable nice and good best excellent outstanding distinction class .... ur my hero ....motta shiva ketta shiva

[@py1918]

Gr8 explanation, sir

[@chalammvs5674]

Glad I liked it ❤️❤️

[@slytheringamer1017]

thanks!🙂

[@yani_tube]

I have a question I’m confused on this question “Which are the two ways that we can represent x and y coordinates of points?”

[@MariosMathTutoring]

Not sure I understand your question...you mean (x,y) ...or maybe in a table ?

[@yani_tube]

Mario's Math Tutoring thanks 😊 I got it correct!!!!

[@MariosMathTutoring]

Great!

[@toymonster7544]

Great!!

[@MariosMathTutoring]

Glad you liked the video!

[@natan1173]

One thing to remember is to find the point plug in the vertex opposite of the line you are making perpendicular

[@soupgodd752]

this is so well explained thank you

[@riopetio7462]

thankyou

[@GusBus2419]

Man now I understand math again

[@Nahjitwhat]

As an eight grader this is really helpful

[@radhakumawat5314]

Thanks

[@samuelm8178]

Thank you

[@MariosMathTutoring]

You're welcome!

[@mokel6105]

youre a legend

[@solaceafk]

ty for helping game man

[@rhitwikprakash1763]

Outstanding

[@eissashami1750]

this takes so much time bruh

[@soggymuffin73]

Thank you for saving my grade on my final

[@vansh8685]

Can someone suggests me method using vector without straight line

[@quaxky326]

Thanks Mario!!!! I have a test next period so thanks for explaining it so well.

[@MariosMathTutoring]

Best of luck!

[@quaxky326]

@@MariosMathTutoring Thank you Mario.

[@igotabadidea2]

wait. So is the way to find circumcentre and orthocentre the same?

[@MariosMathTutoring]

Circumcenter you need to find where the perpendicular bisectors intersect. Orthocenter need to find where the altitudes intersect.

[@aryankhanderia2216]

@@MariosMathTutoring so basically in a equilateral triangle the orthocenter and Circumcenter is same?

[@RvonRentzell]

What if one of your points isn’t a y intercept?

[@RvonRentzell]

@Christiana Simone Mendoza Haha nope just trying to do some 9th grade geometry homework 😅 missed the day we learned it....

[@jtreesor4687]

@Christiana Simone Mendoza im fucked for my finals bro

[@gabrielwiktorowicz3281]

@@jtreesor4687 haha same I missed like 2 weeks I was sick

[@brov3313]

Ive done it over and over and over and i still cant get the answer X(-2,-2), Y(6,10) Z(6,-6) someone help my brain is breaking. can the orthocenter be outside the triangle?

[@jacobblack4001]

If the triangle is obtuse then the orthocenter will be outside

[@brov3313]

@@jacobblack4001 okay thanks

[@user-zi4lc8pf6j]

this is definitely gonna help me with being a lawyer

[@ihavehighcholestorol]

My math teacher went over the whole subject in 30 seconds, so I had no idea what the hell I was doing. Thanks for coming in clutch!

[@MariosMathTutoring]

Glad I could help!

[@MUSIC-pu8el]

This man looks like an NCP but teaches like a Professional 🤓👍 Great Job sir, you're the best🎉🎉

[@meetchokshi1325]

thx

[@lmgwinner6812]

how do we know that the line will go through 1 at 1:49?

[@zebrarockstar6418]

Because the point lies on the y intersect at 1

[@darkphobia9917]

How did u get 10/3 on the Y coordinate????

[@griffenjung9551]

he plugged it into y = 1x +1. 1 times 7/3 is 7/3. add 1 to that (which in this case can also be described as 3/3), and you get 10/3. basically, he just changed the one into a 3/3 and added it with 7/3.

[@darkphobia9917]

@@griffenjung9551 thank you so much man

[@griffenjung9551]

@@darkphobia9917 No problem!

[@griffenjung9551]

@Ritaj Naji because three thirds equals 1.

[@danielwu1388]

@Ritaj Naji ik its 5 months ago, but 3/3=1, and we're using 3 as the denominator since we're adding 1 to 7/3.

[@alexhoops-zd3wn]

that’s soooo hardddd

[@JesseFitzgerald-tf3iw]

Who else is here right before a quiz lol

[@Fleainfested]

This made me almost cry

[@jharanasubedi179]

Why we don't make -5 to +5 like we make -1 to 1 in slope to make perpendicular

[@moosemaen]

since 1 is 1/1 when u flip it, it remains the same. 5 is 5/1 so when u flip it u get 1/5. for both u account for negatives so 1's is -1 5's is -1/5

[@mikeholts2229]

so how can you just say 7/3 is like 3/3 i don’t understand...

[@danielwu1388]

ik its 5 months ago, but he meant that adding 1 to 7/3 is the equivalent to adding 3/3 to 7/3, since 3/3 is 1.

[@StutiKarotiya-yt3yb]

Ceo of Amazon

[@Freya-bz3vl]

im so confused isnt this how you find the circumcentre

[@CoolcookieAud]

Yeah.. I’m confused

[@SurajKumar-xm5fs]

finally i realised today, why indian are intelligent in mathematics, we can do it within a minit..

[@stafey7659]

2:30 Review later

[@aly6015]

I STILL DON’T GET IT WTF I’M LITTERALLY CRYING IM IN HONORS GEOMETRY AND FINALS ARE IN A WEEK AND AHHHHHHH I WANNA DIE

[@anujsarvang433]

If Jeff Bezozs was on Keto.

[@dread_decidueye5782]

This information does not always work, his examples only work if you have a point directly on the y axis

[@aloxxy6221]

what do i do if i dont have a point on the y axis

[@alexdesario9327]

Jesus loves you

[@muhammadzayed7085]

I can't shake the image of someone when I look at him

[@irenegong443]

why am i supposed to care aobut this??

[@Prashant-yp7ob]

Sorry brother you may have been teaching maths good but i am unable to understand your English . I am a Indian student I understand hindi very well.

[@jacksondikeman1385]

have a test on this tommorow scrambling to figure out how to do this its midnight

[@idiot746]

i use slope intercept form y=mx=b instead of point slope form. What do i do if the slope is undefined? (the slope was 0/-9, which i then found the reciprocal of)

[@MariosMathTutoring]

If the slope is undefined then you are dealing with a vertical line …an x= something line …and a perpendicular line to that would be a horizontal line a y= something line….hope that helps

[@ggbearair4630]

Thank you