The distance between two parallel lines given by equation x + 2y - 3 =

Question

The distance between two parallel lines given by equation  x + 2y - 3 = 0  and  2x + 4y - 17 = 0  is approximately:

A. 0.85
B. 1.25
C. 1.95
D. 2.5
E. 3.25

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ShreyasJavahar · Accepted Answer

transform the equations into slope intercept form
1)x + 2y - 3 =0 -> y= -(x/2) + 3/2
2)2x + 4y - 17 = 0 -> y = -(x/2) + 17/4

Since the lines are parallel, you can simply take the difference between the y intercepts to get the distance between the lines

Distance = 17/4 - 3/2 = 11/4 ≈ 2.5.

Also, one could intuitively understand that 11/4 must be greater than 2 and lesser than 3, answer choice (D) -> 2.5

nick1816 · Answer

(1,1) lies on  x + 2y - 3 = 0

Perpendicular distance of (1,1) from  2x + 4y - 17 = 0  
 
=  \frac{|2(1)+4(1)-17|}{\sqrt{2^2+4^2}} 
 
=  \frac{11}{\sqrt{20}}

= \sqrt{\frac{121}{20}}

≈  \sqrt{ 6 }

≈ 2.5

nick1816 · Answer

Difference between the y intercepts is not equal to the distance between 2 lines except when both lines are parallel to x-axis.

Suppose angle ABC = x

Difference between y-intercepts= AB

Distance between the 2 lines= AC

AB*sin(x)= AC

ShreyasJavahar · Answer

Ahh, you're right, my bad. Thanks for pointing it out.

SaikatRoy · Answer

The equations given are
1)x + 2y - 3 =0 
2)2x + 4y - 17 = 0

The same equations in y=mx + c form gives
1) y= -(x/2) + 3/2
2) y = -(x/2) + 17/4

Now both lines being parallel have same slopes.
Also for distance between two lines, the distance between y intercepts is what we need to calculate. 
Hence y intercept putting x=0 gives 3/2 and 17/4. 
Hence Distance = 17/4 - 3/2 = 11/4 or 2.5

Answer choice is (D)

exc4libur · Answer

Distance Parallel Lines:  \frac{|c_2-c_1|}{\sqrt{Aˆ2+Bˆ2}}

Line form:  Ax+By+C  where A,B_1 and A,B_2 must be equal

x + 2y - 3 = 0…2x+4y-6  and  2x + 4y - 17 = 0

A=2, B=4, c_1=-6, c_2=-17

\frac{|c_2-c_1|}{\sqrt{Aˆ2+Bˆ2}}=\frac{|-17-(-6)|}{\sqrt{2ˆ2+4ˆ2}}=\frac{11}{\sqrt{20}}=aprox2.5

Ans (D)

Maria240895chile · Answer

I do not like to use formulas when you can use other method, so basically what I did is draw both lines, find a perpendicular line to both lines, and with equations, points and slope I was able to find a new point at the intersection and then apply the formula for distante of 2 points. See the attachment with the solution.

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The distance between two parallel lines given by equation x + 2y - 3 =

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