Oblicz obwód czworokąta ABCD, jeśli A (-3,1), B=( ,2, -2) C=(6,1) D=2,4

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Odpowiedź :

Odpowiedź:

[tex]A(-3,1)\ \ ,\ \ B(2,-2)\\\\|AB|=\sqrt{(x_{B}-x_{A})^2+(y_{B}-y_{A})^2}=\sqrt{(2+3)^2+(-2-1)^2}=\sqrt{5^2+(-3)^2}=\\=\sqrt{25+9}=\sqrt{34}\\\\\\B(2,-2)\ \ ,\ \ C(6,1)\\\\|BC|=\sqrt{(x_{C}-x_{B})^2+(y_{C}-y_{A})^2}=\sqrt{(6-2)^2+(1-(-2))^2}=\sqrt{4^2+(1+2)^2}=\\=\sqrt{16+3^2}=\sqrt{16+9}=\sqrt{25}=5\\\\\\C(6,1)\ \ ,\ \ D(2,4)\\\\|CD|=\sqrt{(x_{D}-x_{C})^2+(y_{D}-y_{C})^2}=\sqrt{(2-6)^2+(4-1)^2}=\sqrt{(-4)^2+3^2}=\\\\=\sqrt{16+9}=\sqrt{25}=5[/tex]

[tex]D(2,4)\ \ ,\ \ A(-3,1)\\\\|DA|=\sqrt{(x_{A}-x_{D})^2+(y_{A}-y_{D})^2}=\sqrt{(-3-2)^2+(1-4)^2}=\sqrt{(-5)^2+(-3)^2}=\\=\sqrt{25+9}=\sqrt{34}\\\\\\Ob=2\cdot5+2\cdot\sqrt{34}=10+2\sqrt{34}[/tex]