Explicație pas cu pas:
2.
[tex]x_{M} = \frac{4 + ( - 2)}{2} = \frac{4 - 2}{2} = 1\\ y_{M} = \frac{(- 6) + 2}{2} = \frac{ - 4}{2} = - 2 [/tex]
3.
[tex]AB = \sqrt{ {(12 - 9)}^{2} + {(16 - 12)}^{2}} = \sqrt{ {3}^{2} + {4}^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]
[tex]BC = \sqrt{ {(9 - 8)}^{2} + {(12 - 13)}^{2} } = \sqrt{1 + 1} = \sqrt{2} [/tex]
[tex]AC = \sqrt{ {(12 - 8)}^{2} + {(16 - 13)}^{2}} = \sqrt{ {4}^{2} + {3}^{2} } = \sqrt{16 + 9} = \sqrt{25} = 5 [/tex]
=>
[tex]P = AB + BC + AC = 5 + \sqrt{2} + 5 = 10 + \sqrt{2} \\ [/tex]
4.
[tex]MN = \sqrt{ {(0 - ( - 6))}^{2} + {(8 - 0)}^{2} } = \sqrt{ {6}^{2} + {8}^{2} } = \sqrt{36 + 64} = \sqrt{100} = 10[/tex]
[tex]NP =\sqrt{ {( - 6 - 0)}^{2} + {(0 - ( - 3))}^{2} } = \sqrt{ {6}^{2} + {3}^{2} } = \sqrt{36 + 9} = \sqrt{45} = 3 \sqrt{5} [/tex]
[tex]PQ = \sqrt{ {(0 - 4)}^{2} + {( - 3 - 0)}^{2} } = \sqrt{ {4}^{2} + {3}^{2} } = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]
[tex]MQ = \sqrt{ {(0 - 4)}^{2} + {(8 - 0)}^{2} } = \sqrt{ {4}^{2} + {8}^{2}} = \sqrt{16 + 64} = \sqrt{80} = 4 \sqrt{5} [/tex]
=>
[tex]P = MN + NP + PQ + MQ = 10 + 3 \sqrt{5} + 5 + 4 \sqrt{5} = 15 + 7 \sqrt{5} [/tex]
