Hi, I recently learned that to find the tangent at a point on any curve, you can simply place a mirror on that point and reflect the part of the curve on one side of that point such that the reflection flows smoothly into the other part of the curve on the other side. Once this is done, draw a line along the mirror, and this line would be perpendicular to the tangent. However, I do not understand the principle behind this method. How exactly does ensuring that the reflection of one side of the curve flows smoothly into the other side result in the mirror being perpendicular to the tangent? My best guess as of now is that the point must be the point about which the curve is exactly symmetrical, in which case it would make sense that if you reflect one part of the curve into the other part, the perpendicular line which you draw along the mirror would be the line of symmetry. But doesn't this mean that this method would not work if your point is not the point of symmetry? Thank you!