What is the shortest distance from A(3, 5) to the line with equation 3x +2y =6?

Show work and explain please

1 Answer
Jim G.
Dec 4, 2017

#~~3.606" to 3 dec. places"#

Explanation:

#"the shortest distance from a point "(m,n)" to a "#
#"line "Ax+By+C=0" is given by"#

#•color(white)(x)d=|Am+Bn+C|/(sqrt(A^2+B^2)#

#"here "(m,n)=(3,5)#

#"expressing the equation in the correct form gives"#

#3x+2y-6=0#

#"with "A=3,B=2" and "C=-6#

#d=|(3xx3)+(2xx5)-6|/(sqrt(3^2+2^2)#

#color(white)(d)=13/sqrt13~~3.606" to 3 dec. places"#

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