distance of point and line

the distance of the line 3x - y = 6 and P (1, 2)

my attempt : A = 3, B = - 1, C = -6,

d = 3(1) + (-1)(2) - 6/ sq. rt. 3^2 + -1^2

i arrived at sq. rt of 10/ 2.... is this correct? because im so confused when the book's answer is (5/2) sq. rt of 10

i dont know which of this is correct answer. i followed the formula already but they dont have the same answer.

Re: distance of point and line

I agree with your answer. $\displaystyle \frac{\sqrt{10}}{2}$

Re: distance of point and line

We find:

$\displaystyle d=\frac{|3(1)+(-1)(2)-6|}{\sqrt{3^2+1^2}}=\frac{|-5|}{\sqrt{10}}=\frac{\sqrt{10}}{2}$

You are correct.

Re: distance of point and line

why do some books in the formula of a point to a line , the denominator has negative? when will we agree to use the denominator to have negative sign... ?