Determine the distance between the following pair of parallel lines: 4

1.	Determine the distance between the following pair of parallel lines: 4x + 3y – 11 = 0 and 8x + 6y = 15
Answer» Given: The parallel lines are 4x + 3y – 11 = 0 and 8x + 6y = 15 To find: Distance between the givens parallel lines Explanation: The given parallel lines can be written as 4x + 3y − 11 = 0 … (1) 4x + 3y − \(\frac{15}{2}\) = 0 … (2) Let d be the distance between the given lines. ⇒ d =\(\Big\|\frac{-11+\frac{15}{2}}{\sqrt{4^2+3^2}}\Big\|\) = \(\frac{7}{2\times5}\) = \(\frac{7}{10}\) units Hence, distance between givens parallel line is \(\frac{7}{10}\) units

Determine the distance between the following pair of parallel lines: 4x + 3y – 11 = 0 and 8x + 6y = 15

Answer»

Given:

The parallel lines are

4x + 3y – 11 = 0 and 8x + 6y = 15

To find:

Distance between the givens parallel lines

Explanation:

The given parallel lines can be written as

4x + 3y − 11 = 0 … (1)

4x + 3y − \(\frac{15}{2}\) = 0 … (2)

Let d be the distance between the given lines.

⇒ d =\(\Big|\frac{-11+\frac{15}{2}}{\sqrt{4^2+3^2}}\Big|\) = \(\frac{7}{2\times5}\) = \(\frac{7}{10}\) units

Hence, distance between givens parallel line is \(\frac{7}{10}\) units