Question

Suppose that in a certain metric geometry satisfying Axioms D-1-D-3, points A, B, C, and D are collinear and AB = AC = 3,BC = 6,BD = 2,and AD = 1. If the Ruler Postulate is also valid, find CD

Answer 1

Answer:

We calculate that is CD=4.

Step-by-step explanation:

From Exercise we have that

AB=AC=3

BC=6

BD=2

AD=1.  

From Axioms D-1 and D-3, we have  

D-1: ∀ A, B∈ S,  there is a unique AB ∈ R

D-3: ∀ A, B∈ S, AB=BA.

We use the  Axioms D-1 and D-3, and we get that

AC=CA=3

AD=1

because are the points is collinear, we get

CA+AD=CD

3+1=CD

CD=4

We calculate that is CD=4.