Question

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Answer 1

Respuesta:

Explicación paso a paso:

hola

Los cinco casos son rectas paralelas, tienen la misma pendiente r//s

1.  r ≡ 3x - 2y - 2 = 0   ∧   s ≡ 3x - 2y + 1 = 0

2. r ≡ 5x - 6y - 2 = 0   ∧   s ≡ 10x - 12y + 4 = 0≡5x - 6y + 2 =0

3. r ≡ 7x + 3y - 5 = 0   ∧   s ≡ 21x + 9y + 6 = 0≡ 7x + 3y + 2 =0

4. r ≡ 10x + y - 4 = 0   ∧   s ≡ 10x + y + 7 = 0

5. r ≡ 12x - 7y + 2 = 0   ∧   s ≡ 36x - 21y + 9 = 0≡ 12x - 7y + 3 =0

Teoría si  L1 //L2

L1:  ax + by + c1 = 0

L2:  ax + by + c2 = 0

Distancia entre paralelas

$d = \frac{|c_{2} -c_{1} |}{\sqrt{a^{2}+b^{2} } }$

1.  $d = \frac{1 - (-2)}{\sqrt{3^{2}+2^{2} } } = \frac{3}{\sqrt{13} }$

2.  $d = \frac{2 - (-1)}{\sqrt{5^{2}+6^{2} } } = \frac{3}{\sqrt{61} }$

3.   $d = \frac{2 - (-5)}{\sqrt{7^{2}+3^{2} } } = \frac{7}{\sqrt{58} }$

4.   $d = \frac{7 - (-4)}{\sqrt{10^{2}+1^{2} } } = \frac{11}{\sqrt{101} }$

5.   $d = \frac{3 - 2}{\sqrt{12^{2}+7^{2} } } = \frac{1}{\sqrt{193} }$