Question

calcular a distância do ponto P a reta. dada por qual equação
P(-2,5) e r 5x+2y+19=0

Answer 1

$x_{0} = -2, \ y_{0}=5, \ a = 5, \ b= 2, \ c=19\\\\\frac{ax_{0}+by_{0}+c}{\sqrt{a^{2}b^{2} } } \\\\\frac{5.(-2)+2.5+19}{\sqrt{5^{2}2^{2}}}\\\\\--10+10+\frac{19}{\sqrt{5^{2} 2^{2} } }$

$\frac{19}{\sqrt{5^{2} 2^{2} } }\\\\\frac{19}{\sqrt{25+4} }\\\\\\\frac{19}{\sqrt{29} } \\\\\\\frac{19\sqrt{29} }{(\sqrt{29} )^{2} } \\\\\\\frac{19\sqrt{29}}{29}$