Wzór na długość odcinka:
[tex]|AB| = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Poziom A:
a)
[tex]|AB| = \sqrt{(1-1)^2+(4-2)^2} = \sqrt{0+4} = \sqrt{4} = 2\\|BC| = \sqrt{(-2-1)^2+(4-4)^2} = \sqrt{(-3)^2+0} = \sqrt{9} = 3\\|CD| = \sqrt{(-2+2)^2 + (0-4)^2} = \sqrt{0+(-4)^2} = \sqrt{16} = 4[/tex]
b)
[tex]|AB| = \sqrt{(3-1)^2 + (5-5)^2} = \sqrt{2^2+0} = \sqrt{4} = 2\\|BC| = \sqrt{(3-3)^2 + (-2-5)^2} = \sqrt{0+(-7)^2} = \sqrt{49} = 7\\|CD| = \sqrt{(2-3)^2 + (-2+2)^2} = \sqrt{(-1)^2+0} = \sqrt{1} = 1[/tex]
c)
[tex]|AB| = \sqrt{(1-3)^2 + (2-2)^2} = \sqrt{(-2)^2+0} = \sqrt{4} = 2\\|BC| = \sqrt{(1-1)^2 + (0-2)^2} = \sqrt{0+(-2)^2} = \sqrt{4} = 2\\|CD| = \sqrt{(-7-1)^2 + (0-0)^2} = \sqrt{(-8)^2+0} = \sqrt{64} = 8[/tex]
d)
[tex]|AB| = \sqrt{(4-1)^2 + (6-6)^2} = \sqrt{3^2+0} = \sqrt{9}=3\\|BC| = \sqrt{(-2-4)^2 + (6-6)^2}=\sqrt{(-6)^2+0} = \sqrt{36} = 6\\|CD| = \sqrt{(-2+2)^2 + (0-6)^2} = \sqrt{0+(-6)^2} = \sqrt{36} = 6[/tex]
Poziom B:
a)
[tex]|AB| = \sqrt{(2-1)^2 + (5-3)^2} = \sqrt{1^2+2^2} = \sqrt{1+4} = \sqrt{5}\\|BC| = \sqrt{(5-2)^2 + (1-5)^2} = \sqrt{3^2+(-4)^2} = \sqrt{9+16} = \sqrt{25} = 5\\|CD| = \sqrt{(2-5)^2 + (4-1)^2} = \sqrt{(-3)^2+(3)^2} = \sqrt{9+9} = \sqrt{18} = 3\sqrt{2}[/tex]
b)
[tex]|AB| = \sqrt{(-9-3)^2 + (2+3)^2} = \sqrt{(-12)^2 + 5^2} = \sqrt{144+25} = \sqrt{169}=13\\|BC| = \sqrt{(-7+9)^2 + (-2-2)^2} = \sqrt{2^2+(-4)^2} = \sqrt{4+16} = sqrt{20} = 2\sqrt{5}\\|CD| = \sqrt{(-3+7)^2 + (-3+2)^2} = \sqrt{4^2+(-1)^2} = \sqrt{16+1} = \sqrt{17}[/tex]
c)
[tex]|AB| = \sqrt{(-2+2)^2 + (1+2)^2} = \sqrt{0+3^2} = \sqrt{9} = 3\\|BC| = \sqrt{(4+2)^2 + (-7-1)^2} = \sqrt{6^2+(-8)^2} = \sqrt{32+64} = \sqrt{96} = \sqrt{16+6} = 4\sqrt{6}\\|CD| = \sqrt{(-1-4)^2 + (-19+7)^2} = \sqrt{(-5)^2+(-12)^2} = \sqrt{25+144} = \sqrt{169} = 13[/tex]
d)
[tex]|AB| = \sqrt{(2-3)^2 + (-1+2)^2} = \sqrt{(-1)^2+1^2} = \sqrt{1+1} = \sqrt{2}\\|BC| = \sqrt{(1-2)^2 + (9+1)^2} = \sqrt{(-1)^2+10^2} = \sqrt{1+100} = \sqrt{101}\\|CD| = \sqrt{(-1-1)^2 + (4-9)^2} = \sqrt{(-2)^2+(-5)^2} = \sqrt{4+25} = \sqrt{29}[/tex]
Poziom C:
a)
[tex]|AB| = \sqrt{(116-17)^2 + (103-83)^2} = \sqrt{99^2+20^2} = \sqrt{9801+400}=\sqrt{10201} = 101\\|BC| = \sqrt{(176-116)^2 + (23-103)^2} = \sqrt{60^2+(-80)^2} = \sqrt{3600+6400} = \sqrt{10000} = 100\\|CD| = \sqrt{(193-176)^2 + (-121-23)^2} = \sqrt{17^2+(-144)^2} = \sqrt{289+20736} = \sqrt{21025} = 145[/tex]
b)
[tex]|AB| = \sqrt{(-87-13)^2 + (-118-82)^2} = \sqrt{100^2+200^2} = \sqrt{10000+40000} = \sqrt{50000} = \sqrt{25*25*5*16}=5*5*4*\sqrt{5}=100\sqrt{5}\\\\|BC| = \sqrt{(3+87)^2 + (-238+118)^2}=\sqrt{90^2+(-120)^2} = \sqrt{1800+14400} = \sqrt{16200} = \sqrt{100*162}=10\sqrt{9*9*2}=10*3*3*\sqrt{2} = 90\sqrt{2}\\\\|CD| = \sqrt{(43-3)^2 + (-118+238)^2} = \sqrt{40^2+120^2} = \sqrt{1600+14400}=\sqrt{16000} = \sqrt{4*4*4*25*10} = 2*2*2*5*\sqrt{10} = 40\sqrt{10}[/tex]
c)
[tex]|AB| = \sqrt{(-48+18)^2 + (32-8)^2} = \sqrt{(-30)^2+24^2} = \sqrt{900+576} = \sqrt{1476} = \sqrt{4*9*41}=2*3*\sqrt{41} = 6\sqrt{41}\\\\|BC| = \sqrt{(-38+48)^2 + (72-32)^2}=\sqrt{10^2+40^2} = \sqrt{100+1600} = \sqrt{1700} = \sqrt{4*25*17} = 2*5*\sqrt{17} = 10\sqrt{17}\\\\|CD| = \sqrt{(-122+38)^2 + (259-72)^2} = \sqrt{(-84)^2+187^2} = \sqrt{7056+34969} = \sqrt{42025} = \sqrt{25*41*41}=5*41=205[/tex]
d)
[tex]|AB| = \sqrt{(-63+13)^2 + (-97-23)^2}=\sqrt{(-50)^2+120^2} = \sqrt{2500+14400} = \sqrt{16900} = \sqrt{169*100}=13*10=130\\\\|BC| = \sqrt{(41+63)^2 + (-97-23)^2}=\sqrt{104^2 + (-120)^2} = \sqrt{10816+14400} = \sqrt{25216} = \sqrt{16*4*394} = 4*2*\sqrt{394} = 8\sqrt{394}\\\\|CD| = \sqrt{(141-41)^2 + (-450+250)^2} = \sqrt{100^2+(-200)^2} = \sqrt{10000+40000} = \sqrt{50000} = 100\sqrt{5}[/tex]