Question

Qual a distância do ponto P (1,1) a reta "r", cuja a equação é y=-x+3

Answer 1

Resposta:

$reta;\\x+y-3=0\\a=1,b=1,c=-3\\\\ponto;\\P(1,1)\\\\Equacao;\\D=\frac{ax_{p}+by_{p}+c}{\sqrt{a^{2}+b^{2}}}\\\\D=\frac{(1*1)+(1*1)+(-3)}{\sqrt{1^{2}+1^{2}}}\\\\D=\frac{1+1-3}{\sqrt{1+1}}\\\\D=\frac{2-3}{\sqrt{2}}\\D=\frac{-1}{\sqrt{2}}\\\\D=-\frac{1}{\sqrt{2}}*(-\frac{\sqrt{2}}{\sqrt{2}})=\frac{\sqrt{2}}{\sqrt{4}}=\boxed{\frac{\sqrt{2}}{2}}\\\\Distancia=\boxed{\frac{\sqrt{2}}{2}}$

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