ฝัง
- เผยแพร่เมื่อ 11 ก.ย. 2024
- This video contains a proof that the product of the slopes of two lines that are perpendicular is equal to -1.
Visit our website at mathclix.com
Subscribe to get our latest videos: / @mathclix
Like us on Facebook: mathclix
Like us on Google +: plus.google.com/+Mathclix
Follow us on Twitter: @Mathclix
Follow us on Instagram: @Mathclix
“Where Students DO MaTh!”
such a simple proof yet so effective. thank you!
Thank you very much for this clear and beautiful explanation! I've liked the video and subscribed to your channel.
Thanks so much for this video, it's really helpful!
wowwwww, this is the best proof yet
Why aren't you still active on youtube? I really miss ya :(
Hi great video, I would love to see proof to the contrary
Thank you
Thanks! I'm going to use this as an extension for my students after we review pythag!
very nice algebric proof, thanks!
If X-axis and y-axis are also perpendicular, so what is product of their slopes
3:29 Is this m1-m2 because it's the distance between the 2 y coordinates?
m1 means X-axis slope,m2 means Y-axis slope
m
x-axis slope is zero,y-axis slope is infinity then how can you tell that m1m2=-1ano
@@saimalyadri6157 simply. Just look, if x-axis slope (lets say m1) is zero than y-axis slope m2=-1/m1=-infinity as it should be undetemined
why negative slope m 2 is positive?
why m1 - m2 ??
There should be m1=-1/m2. But this simply means that if you use a rotation you will get the system of two equations and you need to express m1 through m2. Ok I also provided explanations for that here th-cam.com/video/1VXtVeUsyT4/w-d-xo.html and actually lots more about Math. You can find also an Oxford entrance test
Coz the point on the y coordinate is (1,-m2) but she didn't mention that in the Cartesian plane. If u wanna get the length of the hypotenuse just add (m1-m2).
Yeah, good! Just use the transformation theory - > rotation 90 degrees
Great explanation i luv it
I love you
Thank you 🙏
What if we replace the X coordinate ( horizontal distance) with 2 or any number instead of 1? I tried so many times and didn't have the slope = -1. I've been struggling with this question for too long, please help me.
Did you figure out a solution?
Just multiply the m1 and m2 by the horizontal distance as well and you'll get -1
For example : if the horizontal distance is 2
The points will be
(2, 2m1) and (2,m2)
The vertical distance will be 2m1-2m2 or 2(m1-m2)
The change in both lengths will be
√4+4m1^2 and √4 +4m2^2
(Do remember that the square root is long here, it is not only on the number 4)
After that use the phytagorean theorem
c^2 = a^2 + b^2
4(m1-m2)^2 = 4 + 4m1^2 + 4 + 4m2^2
4(m1^2-2m1m2+m2^2) = 8 + 4m1^2 + 4m2^2
4m1^2 - 8m1m2 + 4m2^2 = 8 + 4m1^2 + 4m2^2
-8m1m2 = 8
m1m2 = -1
Hope this helps!! ❤
Ty
Non-general, and insufficient, methinks
Thank you