Invariant right angle pair

With a perspective affinity , straight lines are mapped in such a way that the angle between them is generally not maintained. However, there is an affinity for every perspective (not conforming to the angle) and for every point exactly one so-called invariant pair of right angles , i.e. a pair of straight lines through the point whose image lines intersect at right angles in the image point . The Thales' sentence serves as the basis for the construction . The vertical line is intersected with the affinity axis (shown in red in the picture). A circle is drawn through or around this point of intersection . The pairs of right angles (light blue and dark blue) are at right angles to each other. ${\displaystyle P}$ ${\displaystyle P}$ ${\displaystyle P'}$ ${\displaystyle {\overline {PP'}}}$ ${\displaystyle P}$ ${\displaystyle P'}$