parallel lines and shortest distance?

**missionmom** · August 31st 2009, 02:16 PM

Determine the decimal approximation of the shortest distance between the parallel lines. (answer rounded to two deciaml places)
3x+4y-8=0
6x+8y+4=0

Please help me with the steps...
Thank you,

P.S- I keep getting 2 as an answer but im worried im wrong because the question asks for the answer in two decimal aprox.

**pickslides** · August 31st 2009, 03:38 PM

Originally Posted by missionmom

Determine the decimal approximation of the shortest distance between the parallel lines. (answer rounded to two deciaml places)
3x+4y-8=0
6x+8y+4=0

Please help me with the steps...
Thank you,

P.S- I keep getting 2 as an answer but im worried im wrong because the question asks for the answer in two decimal aprox.

$3x+4y-8=0$ ...(1)
$6x+8y+4=0$ ...(2)

These lines are parallel with gradient $\frac{-3}{4}$

The shortest ditance between the lines will lie on the normal between the 2 lines. It will be $y-y_1 = m_N(x-x_1)$ Where $m_N = \frac{4}{3}$ with $x_1 = 0$ and $y_1= 2$

Now we have

$y-2 = \frac{4}{3} (x-0)$ Now find where this line crosses both (1) and (2) and find the distance between these points.

The formula for distacne of a straight line is

$<br /> \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}<br />$

**Plato** · August 31st 2009, 03:38 PM

The distance from the point $(p,q)$ to the line $Ax+By+C=0$ is given by $\frac{|Ap+Bq+C|}{\sqrt{A^2+B^2}}$

So find one point a one of the lines. Then find its distance to the other line.

**missionmom** · August 31st 2009, 05:07 PM

Have i done something wrong here?

y=4/3x+2 y=-3/4x-1/2

[4/3x+2=-3/4x-1/2]x12

16x+24=-9x-6
25x=-30

x=-6/5

y=-3/4(-6/5)-1/2
y=9/10

B(-6/5,9/10) A(0,-1/2)

Im stuck, when i square these points i get 1.3

**pickslides** · August 31st 2009, 05:12 PM

Originally Posted by Plato

The distance from the point $(p,q)$ to the line $Ax+By+C=0$ is given by $\frac{|Ap+Bq+C|}{\sqrt{A^2+B^2}}$

So find one point a one of the lines. Then find its distance to the other line.

Will this method give the shortest distance between two parallel lines?

**sidjaya86** · September 2nd 2009, 03:58 AM

Originally Posted by missionmom

Determine the decimal approximation of the shortest distance between the parallel lines. (answer rounded to two deciaml places)
3x+4y-8=0
6x+8y+4=0

Please help me with the steps...
Thank you,

P.S- I keep getting 2 as an answer but im worried im wrong because the question asks for the answer in two decimal aprox.

The lines are 3x+4y=8
& 3x+4y=-2 ( i have modified the equation by dividing both sides by 2)

The shortest distance between two parallel line in the form

(a1)*x + (b1)*x + c1 = 0
&
(a1)*x + (b1)*x + c2 = 0

will be = mod{ [c1-c2] / [(a1)^2 + (a2)^2]^1/2 }

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