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This
construction is to find out the u-line that maps two given points
to each other under the upper half-plane model. This macro corresponds
to the ‘Perpendicular Bisector’ in Euclidean geometry.
Given:
Two points P1 and P2 in the upper half-plane.
To Construct:
The u-line that reflects P1 to P2 in non-Euclidean
sense.
Constructions:
 Figure 22
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First, let C be the intersection of
 and the
x-axis.
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Construct the perpendicular
bisector of P1 and P2 and which intersects the x-axis at D.
Let r1 be the circle with center D and P1 on its circumference.
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Let M be the intersection
of r1 and the circle with diameter
 , then the semi-circle
(u-line) through M and with C as its Euclidean center is the
mirror u-line.
 Download
This Macro mirror_u_line.mac
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