Question

Fie A,B,C puncte coliniare a.î AB=$\frac{3}{4}$ · AC.Daca AB=9 cm,iar M si N sunt mijloacele segmentelor AB si BC ,calculați MN.

Answer 1

    
[tex]\displaystyle \text{A-----------------------M-----------------------B--------N---------C} \\ \\ AB=9\;cm \\ \\ AB = \frac{3}{4}AC \\ \\ AC = AB : \frac{3}{4} = AB \times \frac{4}{3} = 9 \times \frac{4}{3} = 12\;cm \\ \\ BC = 12 - 9 = 3\; cm \\ \\ MB = \frac{AB}{2} = \frac{9}{2} \;cm \\ \\ BN = \frac{BC}{2} = \frac{3}{2} \;cm \\ \\ MN = MB+BN = \frac{9}{2}+\frac{3}{2}=\frac{9+3}{2} =\frac{12}{2}=\boxed{6\;cm}[/tex]