Question

Reflection about an arbitrary line with equation y=mx + c.

Answer 1

Answer:

There is a formula to calculate reflection about any point

Let the line equation  be ax + by+c = 0 in general in the above case a=-m b=1

and constant c

If we are asked to find the reflection of some arbitary point (x,y) about the line segment and the points after reflection are found to be (p,q) , then the points (p,q) can be found by the below formula

(x-p)÷a =(y-q)÷b= - 2×(ax+by+c)÷(a² +b² + c²)