0

I'm working on a circuit where I copies part of the design, flips it, moves it and rotates it.
The problem is that I did all this manually and don't remember how.

To illustrate, here is the starting position:
enter image description here

Now, the final position after the vertical flip, then the rotation and displacement, looks like a mirror of some unknown axe. enter image description here

The only known information is the before and after coordinates. I'd like to use them to determine the position of a new point.

Moishe Kohan
  • 97,719
Unicorn
  • 103
  • 1
    If a reflection (mirror) takes a point $P$ to a point $Q$, then the midpoint of $\overline{PQ}$ must lie on the line of reflection. Therefore you can calculate the midpoint of the segment joining the old $(x_1,y_1)$ to the new $(x_1,y_1)$ to find one point $A$ on the line of reflection; and the midpoint of the segment joining the old $(x_2,y_2)$ to the new $(x_2,y_2)$ will be another point $B$ on the line of reflection. With those two points $A$ and $B$ you can then find the equation of the line of reflection itself. – Greg Martin Dec 04 '23 at 02:29
  • the slope of the line connecting P and Q is the opposite reciprocal of the slope of the reflection line. you can check my open bounty here for some detail https://math.stackexchange.com/questions/4813193/finding-the-plane-curve-resulting-from-a-reflection-onto-another-plane-curve – vallev Dec 04 '23 at 03:43
  • @GregMartin I'm able to see geometrically the axe, that's all. Can we have a formula with x and y? I basically remember the Cartesian coordinates of the high school so, vallev, sorry but I didn't understand anything. – Unicorn Dec 04 '23 at 12:20

0 Answers0