Dividing a line in a given ratio

author: Martin Marinov
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Българска версия:

D: If point M lies on the line AB and the lenght of the lines AM and BM are m and n (with the same measuring scale), then we say M divides internally AB in ratio m:n, considered from A
AM/MB = m/n or AM:MB = m:n
BM/MA = n/m or BM:MA = n:m

.________._____.
A      ^m      M    ⁿ    B

D: Ratio of the lenghts of two lines, measured with the same measuring scale, is called ratio of two lines

D: If the point M lies on the line AB and is external for the AB and the lengths of AM and BM are m and n, then we say that M divides AB externally in ratio m:n, considered from the point A

          m                                                         n
  ____/\____                                       _____/\____
 /____._____\       AM:MB = m:n        /______.____\     AM:MB=m:n
A        B\_   _/M     BM:MA = n:m       M\__  __/A       B    BM:MA=n:m
               \/                                               \/
                n                                                m

T: If M divides AB (externally or internally) in ratio AM:MB = m:n, then M is the only point with this property