SOLUTION: i have a question if my multiple choice answers for my question find the shortest distance between the parallel lines with equations 5x-12y+33=0 and 5x-12y-6=0 A.3 B.39 C.2

Question 147056: i have a question if my multiple choice answers for my question
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.N/a
how did u come up with the answer 3.25

Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the first equation.

Subtract from both sides.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Simplify.

-----------------------

Now move onto the given equation.

Subtract from both sides.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Simplify.

So when we graph the two equations, we get

Graph of (red) and (green)

Notice how the slope of the two equations is . So the perpendicular slope is . Now simply draw any perpendicular line to the equations. I'm going to graph

Graph of (red) , (green), and the perpendicular line (blue)

Now use any method to find the two intersections. I used a graphing utility to get the two intersections at the points and

Now let's find the distance between the two points. This distance will be the same as the shortest distance between the two lines

Start with the distance formula.

Plug in , , , and . These are the coordinates of the intersections.

Subtract from to get .

Subtract from to get .

Square to get .

Square to get .

Add to to get .

Take the square root of to get .

So our answer is

So the distance between the two points is 3 units.

So this means that the shortest distance between the two lines is also 3 units.

So the answer choice is A)

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
5x-12y+33=0
5x-12y-6=0
.
5x-12y+33=0
-12y=-5x-33
y=5x/12 + 33/12
.
5x-12y-6=0
-12y=-5x+6
y=5x/12 - 1/2
.
The distance between the parallel lines is |33/12 + 1/2|=3.25
This is easier to see if we change the slope from 5x/12 (1st graph) to 0x/12 (2nd graph)

.
Ed
.

.

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