length of hyperbolic lines

[ninagg]

1) Consider 2 points P = (x0, y0) and Q=(x1, y0) on the same horizontalline.
if M is the midpoint of [P, Q] in the euclidean meaning (namely, add thecoordinates of P and Q and divide by 2), check whether or notLH([P,M]) = LH([Q,M]).


2) Consider 2 points P = (x0, y0) and Q=(x0, y1) on the same vertical line.if M is the midpoint of [P, Q] in the euclidean meaning (namely, add thecoordinates of P and Q and divide by 2), check whether or not
LH([P,M]) = LH([Q,M]).
If the length are NOT equal, then find the coordinates of the point N onthe line segment [P, Q] such that LH ([P, N ]) = LH ([Q, N ]).

 

[lookagain]

Please show your work so that we may help you with where you are stuck. Ask some pertinent questions. Please read the rules of posting here: http://www.freemathhelp.com/forum/threads/41539-Read-Before-Posting!!

 

[HallsofIvy]

When you talk about the "Euclidean meaning" of the length of hyperbolic lines, you must be working in one of the Euclidean models for Hyperbolic Geometry, the "disk model", the "half plane model", or the "Klein model". But which one?