Explicație pas cu pas:
A(3,-2), B (-1,4), Q (-1,0)
M mijlocul segmentului AB
a)
[tex]M(x_{M};y_{M})[/tex]
[tex]x_{M} = \frac{x_{A} + x_{B}}{2} = \frac{3 + ( - 1)}{2} = 1 \\ y_{M} = \frac{y_{A} + y_{B}}{2} = \frac{( - 2) + 4}{2} = 1 \\ = > M\left(1 ;1\right) \\[/tex]
b) ΔBQM:
[tex]BQ = \sqrt{ {( - 1 - ( - 1))}^{2} + {(0 - 4))}^{2} } \\ = \sqrt{0 + 16} = \sqrt{16} = 4 [/tex]
[tex]BM = \sqrt{ {(1 - ( - 1))}^{2} + {(1 - 4)}^{2} } \\ = \sqrt{4 + 9} = \sqrt{13} [/tex]
[tex]QM = \sqrt{ {(1 - ( - 1))}^{2} + {(1 - 0)}^{2} } \\ = \sqrt{4 + 1} = \sqrt{5}[/tex]
→
[tex]P_{(BQM)} = BQ + BM + QM \\= 4 + \sqrt{13} + \sqrt{5} < 10 \\ [/tex]
