Question

Determine a distancia do ponto a ( -2, 3) à reta r : 3x + y - 2 = 0

Answer 1

Resposta:

√10 / 2

Explicação passo-a-passo:

• De acordo com a formula de distancia da reta ax + by + c ao ponto (x,y):

r : 3x + y - 2 = 0

a = 3

b = 1

c = -2

A: (-2 , 3)

x = -2

y = 3

$d=\frac{|ax+by+c|}{\sqrt{a^{2}+b^{2}}} \\\\d=\frac{|3(-2)+1(3)-2|}{\sqrt{3^{2}+1^{2}}} \\\\d=\frac{|-6+3-2|}{\sqrt{9+1}} \\\\d=\frac{|-5|}{\sqrt{10}} \\\\d=\frac{5}{\sqrt{10}} \\\\d=\frac{5\sqrt{10} }{10}\\ \\d=\frac{\sqrt{10}}{2}$

Espero ter ajudado!