Question

Calcule a distancia do ponto P(2,6) a reta 3x-4y-2=0          
a) 32 b)10 c)8  d) 4 e)2

Answer 1

P (x, y)
r: ax + by + c = 0

P (2, 6)
r: 3x - 4y - 2 = 0

x = 2
y = 6

a = 3
b = -4
c = -2

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$d = \frac{| ax + by + c |}{ \sqrt{ a^{2} + b^{2} } }$

$d = \frac{| 3.2 + (-4).6 + (-2) |}{ \sqrt{ 3^{2} + (-4)^{2} } }$

$d = \frac{|6-24-2|}{ \sqrt{9+16}}$

$d = \frac{|-20|}{ \sqrt{25} }$

$d = \frac{20}{5}$

$d = 4$

Alternativa D