Thread: parallel lines and shortest distance?

1. parallel lines and shortest distance?

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

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.

2. 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

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

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

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

Now we have

$\displaystyle y-2 = \frac{4}{3} (x-0)$ 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

$\displaystyle \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

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

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

4. 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

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

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?

6. 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

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 }