Reflect a Point Over a Line (Algebraically)

Learn how to find the image point of a point reflected over a line using algebraic methods. We discuss how to use the slope, the perpendicular slope, midpoint, and the point slope form equation of a line to find the coordinates of the point after it is reflected.

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[advitgarg]

been at this for some time... best 5 min i spent today! went from very confused to crystal clear

[Eldiosqueprovee]

Once again, much love for your videos I as an individual want to pay my respect for the way you cut to the chase with no words that are all over the map but that are straight to the point

[jay-learnzoe]

You've been so knowledgeable. Your explanations are clear. Thank you.

[veerchulki]

Man, we've been working on this for a week now and I finally understood it right before the test with this video. Thank you!

[vickysahagian]

Mario I said this last year I’ll say it again ily😍 you are my icon u saved my math grade man❤️❤️

[sungjinhong]

Thank you for this video. I am watching it on December 9th 2020 which coincidentally is the 1 year anniversary of it. It helped me get ahead in math class and I really want to thank you for making these.

[avdhootkasture]

Thanks mario for your help . Was always in need for someone like you who could help improve my mathematics

[nmtwarreng]

This was absolutely amazing, man. THANK YOU!!

[Burgerhero]

Thank you so much for explaining this clearly! I had a situation that was too complicated to solve by graphing, and no matter where I looked I couldn't find a calculator that would work with the line I reflected over. This allowed me to solve it myself and get an exact answer!

[ocgcg]

So helpful. And thanks man thanks to you I have an A in class. And now I understand a lot. Now to me it's just to know how to move numbers and that's it. So easy now. Thanks 🙋‍♂️🤓😅😅

[gauravnegi]

Thank you this was sooo easy to get. Khan Academy just told graphical method and that too for integer points and simple reflection lines so i didn't knew the algebraic method.

[softlanding]

Thank you for your help! I have been stuck in a project for 5 days and your explanation helped me find where I was wrong!

[Digsanime]

Best reflection video for maths easily

[henok.l]

Ima a little late but this helped me a lot thank u for posting this man❤🎉

[lefishe]

this video deserves more likes and views :)

[prashanthigunarathna]

Thank you sri !, your explanation was very clear.

[kazishahjalal]

Thank you sir. This method is very clear to me now.

[onaokeke]

Amazing, thank you so much. From a fellow tutor

[soviet-kermit]

May I ask a question? Point A has co-ordinates (-4, 3) point A is reflected on the line y=2 the co-ordinates of image A please someone help what do I do to solve this problem

[atomictraveller]

a more complex but tangible application.. 2D ray tracing (ideal specular) reflection on a line from point Tx to Rx.. the point on the line where the incident angles to the normal match and so yield a unity reflective gain is easily found by dividing the distance of each point from the line.
by modeling reflections along the line and storing the length of each path as magnitudes of samples in an impulse (time data, thereby constructing a "wave sample" of the idealised reflection impulse), the reflection from the unity gain point to either direction appears to form an exponential decay, possibly truncated by the length of the line/segment/wall.
so conceptualised as two exponential envelopes from the point of shortest reflection, how can they be meaningfully combined to form a single impulse. the problem to me is, the first sample of each envelope represents the gain at the unity point. a meaningful impulse combining the two envelopes would have the same amplitude at this point. however, the tail of each envelope, being possibly truncated and thus "meaningful", need to be represented at their original amplitude.
i referenced lambert's cosine law of diffuse reflection (different case) and found "a statement indicating cosine properties to specular reflection" which seems reasonable since reflection seems sensibly dipole.
it's an interesting problem to me because it seems to be a product of the abstraction. i probably haven't picked up enough calculus from audio programing to understand the problem of deriving an impulse for the reflection more wholistically. if you're interested in thinking about it and perhaps suggesting something i ought to reference, thank you!
there are a few methods that occur to me to "solve" this in dsp, but none have theoretical basis.