Worksheet: Distance between Parallel Lines

In this worksheet, we will practice finding the distance between any two parallel lines in the coordinate plane given their equations.

Q1:

What is the distance between the parallel lines 𝑥 6 𝑦 + 1 1 = 0 and 𝑥 6 𝑦 + 2 2 = 0 ?

  • A 1 1 3 7
  • B 3 5 3 7 3 7
  • C 1 1 5 5
  • D 1 1 3 7 3 7

Q2:

What is the distance between the parallel lines 3 𝑥 𝑦 + 5 = 0 and ( 8 , 7 ) + 𝑠 ( 8 , 2 4 ) ?

  • A 9 2 length units
  • B 1 0 2 length units
  • C 1 8 length units
  • D 1 8 1 0 5 length units

Q3:

Find, to the nearest hundredth, the distance between the parallel lines 𝐿 𝑥 + 7 9 = 𝑦 + 1 5 = 𝑧 7 6 1 and 𝐿 𝑥 + 3 9 = 𝑦 + 1 0 5 = 𝑧 + 1 0 6 2 .

Q4:

Determine the shortest distance between the two parallel lines whose equations are 𝑦 = 4 and 𝑦 = 4 .

Q5:

Find the shortest distance between the two parallel lines with equations 𝑦 = 2 𝑥 7 and 𝑦 = 2 𝑥 + 3 .

  • A 2
  • B 2 2
  • C 4 2
  • D 2 5
  • E 5 2

Q6:

The distance between two parallel lines is 3 7 . If a third line is perpendicuar to both these lines, and intersects them at the points 𝐴 ( 𝑎 , 2 ) and 𝐵 ( 1 0 , 3 ) , find all possible values of 𝑎 .

  • A 𝑎 = 4 6 or 𝑎 = 2 6
  • B 𝑎 = 1 6 or 𝑎 = 4
  • C 𝑎 = 2 6 or 𝑎 = 4 6
  • D 𝑎 = 4 or 𝑎 = 1 6

Q7:

What is the distance between the parallel lines 2 𝑥 + 7 𝑦 2 2 = 0 and 2 𝑥 + 7 𝑦 + 4 4 = 0 ?

  • A 6 6 5 3
  • B 9 4 5 3 5 3
  • C22
  • D 6 6 5 3 5 3

Q8:

What is the distance between the parallel lines 3 𝑥 + 4 𝑦 + 1 1 = 0 and 3 𝑥 + 4 𝑦 2 2 = 0 ?

  • A 3 3 2 5
  • B 4 9 5
  • C 3 3 7 7
  • D 3 3 5

Q9:

What is the distance between the parallel lines 𝑥 3 𝑦 1 0 = 0 and 𝑥 3 𝑦 2 0 = 0 ?

  • A1
  • B 2 1 0 5
  • C 5 2
  • D 1 0

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