How to calculate the mirror point along a line?

Question

In 2D plane, I have a point and a line. How to get the mirror point along this line?

Answer 1

You can use a simple formula to find this. First you have to write the formula of the line using

ax+by+c=0

lets say your line is y=x. and the point you'r trying to mirror is (3,2). we all know it's gonna become (2,3) anyway write y=x in standard form, which will become like this :

y-x=0

now use this formula and insert the values of the point instead of the x and y.

    (ax+by+c)/a^2+b^2
    (a^2 means a square.)

you will get a value, so let's name it K. in this instance where the point is (3,2) and the line is y-x=0, K would equal to:

(-3+2)/(1+1)= -1/2

now to calculate the new coordinates all you have to do is insert the values in this formula:

 x-2ak
 y-2bk

where x and y are the original coordinates and a and b are the values used in the original formula of the line (y-x=0 a=-1, b=1, c=0) so the value we get is:

3 - 2 x -1 x -1/2 = 3-1 = 2
2 - 2 x +1 x -1/2 = 2+1 = 3