SOLUTION: Find the shortest distance between the parallel lines with equations 5x-12y+33=0 and 5x-12y-6=0. a. 3 b. 39 c. 27/5 d. 27/13 e. nota i love receiveng all the work step b

Question 146644: Find the shortest distance between the parallel lines with equations 5x-12y+33=0 and 5x-12y-6=0.
a. 3
b. 39
c. 27/5
d. 27/13
e. nota
i love receiveng all the work step by step it really helps me know where to get started and how to continue im sending different types of problems to help me with those sections of math .THANK YOU!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The answer is d, 27/13. I'm looking for a better way to solve this, but this is how I did it.
Solve for the slope and the 2 y-intercepts by putting both eqns in the form y = mx+b.
The slope of both is 5/12, and one y-int is -1/2, and the other is -11/4.
So they're 9/4 apart on the y-axis.
They form a right triangle with the X and Y axes. Since the slopes are 5/12, the sides are in the ratio of 5 (on the Y axis) to 12 (on the X axis), and the hypotenuse is 13.
Making another right triangle by connecting the 2 lines from either on the Y-intercepts gives a similar triange with the same ratios, 5, 12 and 13.
The distance between the 2 Y-intercepts is 9/4, and the long side of the triangle is 12/13 of that, so it's 12/13 times 9/4, which is 108/52, or 27/13.
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I'm sure there's a more straightforward to do this. I'll look for it, and if you email me I'll send you what I figure out.
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