Question

Dado o ponto P (3,2), determine a distância de P até a reta r, nos seguintes casos:
a)r: x=-1
b)r:y-4=2/5 (x-3)...

Agradeço desde já...

Answer 1

a)
x =  -1
-1 - x = 0

$D = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}} \\ \\ D = \frac{|-1.3 + 0.2 - 1|}{\sqrt{1^2 + 0^2}} \\ \\ D = \frac{|-3 - 1|}{\sqrt{1}} \\ \\ D = \frac{|-4|}{1} \\ \\ D = 4$

b)
 
y - 4 = 2/5(x - 3)
y - 4 - 2x/5 + 6/5 = 0 
5y - 20 + 2x + 6 = 0
5y - 2x -14 = 0 

$D = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}} \\ \\ D = \frac{|5.2 + (-2).3 -14|}{\sqrt{(-2)^2 + 5^2}} \\ \\ D = \frac{|10 - 6 - 14|}{\sqrt{4 + 25}} \\ \\ D = \frac{|10 - 20|}{\sqrt{29}} \\ \\ D = \frac{|-10|}{\sqrt{29}} \\ \\ D = \frac{10}{\sqrt{29}} = \frac{10 \sqrt{29}}{29}$