Question 1180629
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Find the distance d between two parallel lines 3x - y + 2 = 0 and 3x - y + 7 = 0.
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                Thank you for asking.



<pre>
If two parallel lines in a coordinate plane are given by equations


    ax + by + e = 0

and

    ax + by + f = 0,


then the distance between these parallel lines is


    d = {{{abs(e-f)/sqrt(a^2 + b^2)}}}.


See this Wikipedia article

    https://en.wikipedia.org/wiki/Distance_between_two_parallel_lines#:~:text=The%20distance%20between%20two%20parallel,distance%20between%20them%20is%20zero.



In your case,  a = 3;  b = -1;  e = 2;  f = 7.


So, according to the formula above, the distance between the given parallel lines is


    d = {{{abs(7-2)/sqrt(3^2 + (-1)^2)}}} = {{{5/sqrt(10)}}} = {{{(5*sqrt(10))/10}}} = {{{sqrt(10)/2}}} = 1.581  (rounded).    <U>ANSWER</U>
</pre>

Solved, answered and carefully explained.