How to Find Circumcenter Given 3 Vertices (Algebraically)
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- Опубликовано: 15 окт 2024
- Learn how to find the circumcenter given 3 vertices of a triangle algebraically in this math video tutorial by Mario's Math Tutoring. We discuss what the circumcenter is and how to find it. This particular problem involves using the midpoint formula, slope formula, perpendicular slope, and point slope form of a line.
0:09 What is the Circumcenter?
0:55 Significance and applications of the circumcenter
1:26 Find the midpoint of the side
2:17 Find the Slope of the side
2:45 Find the perpendicular slope
3:07 Use Point Slope Form of a Line to write equation of perpendicular bisector.
3:58 Find the Midpoint of a second side of the triangle
4:31 Find the slope of the second side
4:53 Find the Perpendicular slope of the second side
5:00 Write the equation of the perpendicular bisector
5:44 Using substitution to solve the system of equations and find the circumcenter
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Your explanation was way easier than my teachers... or I just took the time to study, thank you!
who else here because school doesn't teach this to them correctly
i’m on quarantine right now and my teacher got fired and they expect me to take a test via zoom tomorrow i’m gonna die 💀
i just didtn take online class seriously but also that
my teacher literally gave us the worksheets and told us to figure it out in breakout rooms
yes...
@@alicezhou6328 half my class is failing
The way I learned more here in less then 10 minutes then I did sitting at my laptop for hours
IKR so helpful
Aren't you watching this on your laptop too?
I was sitting for 2 hours in front of my laptop finding the answers and then finally got the concept.
@@a_dash2 Yeah, back then I was complaining about my online teacher's method of teaching. Looking back on it he did try and I'm sure he was thrown into a loop too with the pandemic and all.
savvas?
i learn more from this man's channel than my high school geometry teacher
This man is single handedly holding my grade up!
ikr :)
Bro my math class has been confused about this because our teacher doesn’t know how to teach it. This guy just taught to me in seven minutes💀
Great explanation once again, thanks!
Glad you liked the video!
Doing honors geometry over the summer and tbh all your videos have been a god send, since the pace of my class is just a bit to fast to really understand anything.
This man teaches me stuff in half of the time my teacher can, and he does it better
It can also be done by distance formula since all the vertices are at equal distance from it so we can easily get 2 equations fir two variables.
But great alternative though
A straight forward way to solve for the circumcentre (a.b) is to solve for a.b from(a-x1)^2+(b~y1)^2=(a~x2)^2+(b~y2)^2=(a~x3}^2+{b~y3)^2. (xi,yi) being the vertices I =1,2:3 you will get two linear equations in a and b .solving them is easy
I'm in 7th grade, an when I first learned this, I was totally confused on how to solve this, since my teacher explained it so vaguely, and basically said, "You're on you're own now, kid!" This explanation was amazing, and saved my grades. Tysm
Glad it helped!
Why can't you be my Math teacher?
pretty sure he is
This was so helpful thank you
its odd how I can be confused for an entire year then come here and suddenly know everything I honestly do not know why I always wait to turn to this channel when I am about to fail a final. If I used this channel more I could be doing calc by now
thank you man, my teacher gave us the question without even showing us how to do do it
you are saving my life right now
Nice Explanation,
Try tutorials for Higher secondary maths also : )
mr pak has sent me to this place
i'm watching from india and you are teaching great
mario, youre amazing
Thanks mister, im in 8th grade and i have a test tomorrow., This helped.
Best video ever!!!!
Thank you for this video and explanation. In my Saxon Geometry book it doesn't explain it either, but why don't you also find the midpoint (and then slope and perpendicular) of line AC? Or maybe I should ask, does it matter which 2 midpoints (and slope and perpendicular) you choose to find?
well, it doesn't matter which two midpoints you choose to find. As for your first question, the point of intersection of two lines will not differ if you add a third line, meaning you only need to find the point of intersection of two perpendicular bisectors.
amazing vid. thank you Mario!
THANK YOU!!!! with my test in 2 days I still couldn't understand this until now
Sir how to find circumcenter when in 3d geometry where z axis is included
how about getting out two perpendicular equation going through the middle point of two arms of the triangle and solving them?
Keep working......u r doing great
Thanks Kamil! Glad you like my videos!
This really helped! Thanks!:)
bru me trying to get how to do this in 1 hr
@@enbaoliang6938 actually though
this guy taught me more in 10 mins than my teacher did in 6-7 class periods
in that formula , what if m = (yA - yB)/(xA - xB) when xA - xB or yA - yB equal 0?
Thank you so much, I was literally dying before this
thank you for your explanation
You are welcome!
What do you do if your slope is dividing by zero
yo your the goat for this
Thanks for this video it helped me witih my homework
This just saved me from my quiz
This is sooooooo helpful!
You’re very helpful thank you !
Thank you sir
You’re welcome!
Thank you sir❤
Thank you so much
Thank you sir 🙏
can't you convert the fraction into decimals and then go from there?
thanks dude
Thanks
thanks bestie ❤
can't we simply find a point equidistant from all 3 vertices using distance formula
Thanks very helpful!
tysm I really appreciate it
Love from India
how about the center of circle in tringle
Incenter…find where the 3 angle bisectors intersect.
@@MariosMathTutoring the question is find the center of a circle incenter like you said and we have only the a .b .c the adges of the tringle
and thanks for replay
Can you PLEASE do this for GEOMETRY? PLEASE?!!
THANK YOU!!!
If an edge is purely vertical, you end up with -(1/0) as a slope, which obviously simply don't work. Is there a method that could work for any A, B and C?
what are you talking about? a slope of 0/1 is a horizontal line
yeah, and if you divide by 0, mathematics tend to not like that@@dbdmthepulse
@@tsunayoshisawada8062 1/0 is just a vertical line, the perpendicular of that would be 0/1 which is just a horizontal line. This method does work with any value as long as you keep in mind the perpendicular to a purely vertical line, is a purely horizontal line.
So... it doesn't work for every value since one of them is a special case...@@dbdmthepulse
U saved me for my finals
Is this in a level?
Ur legend for true
could you only find two lines?
Yes
Can we solve that by circle formula :(x-h)²+(y-k)²=R² ?
Yes asha we can but if you don't know about slopes but it's a long process and we can use it because circumcentre is equidistance from vertices hope you doing well 👍🙏
Any Indian here 🙄❤️
Yeah ११th std student
Same bhai
Want such teacher in our school
Why side AC SLOPE AND MID POINT YOU HAD NOT FIND
You taught me how to do this in 7 minutes, and school failed me after an hour of trying
Lmao I was looking for help on a problem and these are literally the EXACT POINTS
At 4:43 he did something wrong, the B vertices must be X1, Y1 and the C Vertices must be X2 Y2, when he replaced them both, the entirety of this is false.
Mr. Pak sent me to this place
I tried lime AC and I got a different answer
Thanks for the amazing lecture
Jeff Bezos
(just kidding 😁)
1 -2
Jeff bezos is teaching math
I have the attention span of a 1 month old baby so I had to rewatch this so many times 😔
Baldi basics
Bro gonna chase me around with a ruler
yesser
I got lost sadly
Jeff Bezos
thavnmk
This doesnt help at all talk slower and write down the equations used and how they matter
I hate geometry I want to quit school cuz of it
Isn't it supposed to be -1/4 for M (perpendicular) BC and for the fraction simplification 4 has to multiply with 3. Other than that thank you, I was struggling with this in my Geometry class and this made me understand
mr pak has sent me to this place
Thank you!