Point coordinate in the form of the x+iy form
ax+by+c=0 straight line coefficients through a gap

The set point with coordinates (X+Yi)
point coordinates
The set straight line
Coordinates of a mirror point
coordinates of the resulting point

Calculation of new coordinates of the set point or points which are specularly displayed concerning any set straight line is considered. 


пример зеркальной точки

The algorithm for finding the coordinates of the mirror point is very simple

1. Determine the point of intersection of the abscissa axis and the line

2. Regarding this point, we make a rotation by an angle equal to the angular coefficient of the line.

How this is done can be found in the material turning points at an arbitrary angle 

3. Using the view matrix  matrix example, we obtain a mirror image of the point relative to the abscissa axis.

4. Make a reverse turn (as in paragraph 2)

5. We get the result.

Mathematically, the solution of the problem is a product of three matrices, if the point around which the rotation is made is at the origin

mirroring formula


Consider the implementation of this algorithm using the example shown in the figure above.

So, we have a point with coordinates C (-2,6) and the equation of the line -18.8x + 47.11-42.35 = 0

Enter the data 

The coordinates of point C are written here in this form -2 + 6i

The coefficients of the line are written through the space -18.8 47.11 -42.35

We get the answer

Given point with coordinates (X: Y)
point coordinates
Direct line
Mirror Point Coordinates
coordinates of the resulting point

As you can see, this coincides with the graph at the beginning of the article made with geoGebra.

Good calculations !!

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