Odpowiedź:
z.1
A = ( 2, -3) B = (0, 1)
xs = [tex]\frac{2+0}{2}[/tex] = 1 ys = [tex]\frac{-3 + 1}{2}[/tex] = - 1
S =( 1, - 1)
I A B I² = ( 0 - 2)² + ( 1 - (-3))² = 4 + 16 = 20 = 4*5
I AB I = [tex]\sqrt{20}[/tex] = 2√5
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z.2
M =( 2, -1) N = ( 4, 5)
a = [tex]\frac{5 -(-1)}{4 - 2}[/tex] = [tex]\frac{6}{2}[/tex] = 3
y =a x + b
y =3 x + b i N =( 2 , -1)
więc - 1 = 3*2 + b
- 1 = 6 + b
b = - 7
Odp. y = 3 x - 7
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z.3
l : 2 x + y - 5 = 0
y = -2 x + 5
y = [tex]\frac{1}{2}[/tex] x + b - dowolna prosta prostopadła do danej, bo -2*[tex]\frac{1}{2}[/tex] = -1
P = ( -4, 1) więc 1 = [tex]\frac{1}{2}[/tex]*(-4) +b
1 = -2 + b
b = 3
y = [tex]\frac{1}{2}[/tex] x + 3 - postać kierunkowa
lub [tex]\frac{1}{2}[/tex] x - y + 3 = 0 / *2
x - 2 y + 6 = 0 - postać ogólna
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z.4
k : x + 2 y - 3 = 0 i l : y = 2 x + 4
więc
x + 2*( 2 x + 4) - 3 = 0
x +4 x + 8 - 3 = 0
5 x + 5 = 0
x = - 1 y = 2*(- 1) + 4 = -2 + 4 = 2
P =( - 1, 2)
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z.5
a) ( x - 2)² + ( y + 7)² = 9
S = ( 2, - 7) r = √9 = 3
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b) x² + y² - 10 x + 8 y -1 = 0
( x - 5)² - 25 + ( y + 4)² - 16 - 1 = 0
( x - 5)² + ( y + 4)² = 42
S = ( 5, - 4) r = [tex]\sqrt{42}[/tex]
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Szczegółowe wyjaśnienie:
