In the upper-plane plane model for hyperbolic geometry, calculate the distance between the points A(0, 4) text{and} B(3, 5). Give your answer accurate to three decimals. Hint: Recall the definition of distance in the upper-half plane model.

sjeikdom0 2021-02-10 Answered
In the upper-plane plane model for hyperbolic geometry, calculate the distance between the points A(0, 4) and B(3, 5). Give your answer accurate to three decimals. Hint: Recall the definition of distance in the upper-half plane model.
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Expert Answer

Liyana Mansell
Answered 2021-02-11 Author has 97 answers
Step 1
We have the two points A(0, 4) and B(3, 5) let
A=(0,4)(x1,x2)
x1=0,x2=4
B=(3,5)(y1,y2)
y1=3,y2=5
We have distance,
dis(x1y1x2y2)
=2ln((x2x1)2+(y2y1)2+(x2x1)2+(y2y1)22y1y2)
Substitute the values
=2ln((40)2+(53)2+(40)2+(53)223×5
Step 2
=2ln(42+32+42+82215)
=2ln(16+9+16+64215)
=2ln(25+80215)
=2ln(5+80215)
80=16×5
=16×5
=45
=2ln(5+45215)
=2ln(13.944071917.7459666924)
=1.18355406
=1.184
So the answer is 1.184
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