SOLUTION: Find the distance d between two parallel lines 3x - y + 2 = 0 and 3x - y + 7 = 0 Note. I didn’t really know if I should place this on the distance category or the points and l

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Question 1180629: Find the distance d between two parallel lines 3x - y + 2 = 0 and 3x - y + 7 = 0
Note. I didn’t really know if I should place this on the distance category or the points and lines category, so I’m sorry. Can you please show your full solution? Thank you!
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
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parallel lines 3x - y + 2 = 0 and 3x - y + 7 = 0
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Not the only method, but:

slope of the two given lines, . Slope for any line perpendicular to them, . Pick any point on one of the given lines you want. Find equation of PERPENDICULAR line containing that point. Find where this intersects the OTHER GIVEN line. Now, use the distance formula to find distance between these two points.
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
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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. 


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 = .


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 =  =  =  =  = 1.581  (rounded).    ANSWER

Solved, answered and carefully explained.



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