Linear Algebra: Reflection in any Linear Line y=ax+b

Today, we use matrix transformations to derive a formula which we can use to reflect any point on a plane in the any linear line of the form y=ax+b (or y=mx+c).
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[@eng360]

How can this channel be underrated ?

[@xondiego]

Beautifully presented. Makes sense... Far better how is presented in books. Excellent working guys.

[@qncubed3]

Thanks! :)

[@peterhall6656]

This is an important technique especially when it comes to rotation matrices in 3 d. Very clear explanation. Top marks! My only comment is that R^(-1}(theta) = R(-theta). The standard R(theta) is for counterclockiwse rotations so you use -theta for the clockwose rotation. No need to calculate an inverse but having done so you get the general relation anyway.

[@Thepeacegames]

The rotation matrix is orthonormal, so the inverse will simply be the transpose

[@sebasn6751]

thank YOUUUU you just saved my lineal algebra exam thatnkk youuu so muchh

[@sufiyansadiq9962]

you made the concept look sooooooooooooooooooooooooooo obvious, i instantly subscribed
keep up the good work.

[@Sarmadness]

Great explanation, thanks!

[@jesuschrist6424]

TERRIFIC video, although I have a quick question. How would you express this as a matrix transformation, rather than just the formula images of the points. What I mean is something like [x,y][Matrix]=[x',y']

[@cherylann1632]

Awesome explanation. Clear concise and beautifully presented. Thank you . I instantly subscribed !

[@shubhamshirode5911]

Wonderful explanation 🔥🔥

[@darcash1738]

so for y = -x, it would be [[0, -1], [-1, 0]]?

[@marrom6808]

If i want to reflect relative to what a is, i.e. if y = x then a = 1 and then we have ((1, 0), (0, -1)), does this mean ((1,0),(0,-a)), so i.e. a = 2 means ((1,0), (0, -2)) ?

[@surjo8095]

Underrated af

[@tenzindalha5852]

You're a beast bro, thanks so much!

[@sigmainclination9483]

Great video 💯❤

[@thegamingtaco6283]

I have a question, is there a particular matrix that will allow you to reflect a vector across this plane (x+y+z=1)

[@Sean-dm8ez]

incredible video

[@gravygod9820]

Awesome derivation!

[@chrizbg2438]

Hizo una buena deducción de una fórmula que permita reflejar un P(x,y) a través de una recta y=mx+b, pero le faltó probar con un ejemplo la fórmula.

[@solaris413]

can't be it done in easy way like first we will find a perpendicular to given line by using slope property (m1*m2 = -1) , y - mx = k then we will insert the point coordinates which has to reflected (x1,y1) we will get a perpendicular which passes through (x1,y1) then we will get foot of perpendicular, which is the mid-point between reflected point and original point so we can easily get it

[@user-ug2us2dh2u]

could you show the vector formula as well?

[@qncubed3]

Which formula are you referring to?

[@Jay_Sunghoon_Jake]

can i use y=x reflection instead of x axis reflection?