Distance between the parallel lines

1. Find the distance between the parallel lines with equations \(2x + 3y - 5 = 0\) and \(2x + 3y + 7 = 0\)

2. Calculate the distance between the lines represented by the equations \(4x - 3y + 6 = 0\) and \(8x - 6y + 12 = 0\)

3. Determine the distance between the lines given by \(3x + 2y - 4 = 0\) and \(6x + 4y - 8 = 0\)

4. Find the distance between the lines described by \(5x + 2y + 1 = 0\) and \(5x + 2y - 3 = 0\)

5. Calculate the distance between the parallel lines represented by \(2x - 3y + 5 = 0\) and \(4x - 6y + 10 = 0\)

6. Determine the distance between the lines with equations \(3x - 4y + 7 = 0\) and \(6x - 8y + 14 = 0\)

7. Find the distance between the lines defined by \(2x + y - 3 = 0\) and \(4x + 2y - 6 = 0\)

8. Calculate the distance between the lines given by \(3x - 5y + 1 = 0\) and \(6x - 10y + 2 = 0\)

9. Determine the distance between the parallel lines described by \(4x - 2y + 8 = 0\) and \(8x - 4y + 16 = 0\)

10. Find the distance between the lines represented by \(6x + 8y - 10 = 0\) and \(3x + 4y - 5 = 0\)

ANSWERS 

1. \(\displaystyle \frac{12}{\sqrt{13}}\) units.

2. \(\displaystyle \frac{6}{5}\) units.

3. \(\displaystyle \frac{4}{\sqrt{13}}\) units.

4. \(\displaystyle \frac{4}{\sqrt{29}}\) units.

5. \(\displaystyle \frac{5}{\sqrt{13}}\) units.

6. \(\displaystyle \frac{7}{\sqrt{25}}\) units.

7. \(\displaystyle \frac{3}{\sqrt{5}}\) units.

8. \(\displaystyle \frac{1}{\sqrt{34}}\) units.

9. \(\displaystyle \frac{8}{\sqrt{20}}\) units.

10. \(\displaystyle 1\) units.