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Lesson: Distance between Parallel Lines

Sample Question Videos

Worksheet • 9 Questions • 1 Video

Q1:

What is the distance between the parallel lines π‘₯ βˆ’ 6 𝑦 + 1 1 = 0 and π‘₯ βˆ’ 6 𝑦 + 2 2 = 0 ?

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

Q2:

What is the distance between the parallel lines βˆ’ 3 π‘₯ βˆ’ 𝑦 + 5 = 0 and ( βˆ’ 8 , βˆ’ 7 ) + 𝑠 ( βˆ’ 8 , 2 4 ) ?

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

Q3:

Find, to the nearest hundredth, the distance between the parallel lines 𝐿 ∢ π‘₯ + 7 9 = 𝑦 + 1 5 = 𝑧 βˆ’ 7 βˆ’ 6 1 and 𝐿 ∢ π‘₯ + 3 9 = 𝑦 + 1 0 5 = 𝑧 + 1 0 βˆ’ 6 2 .

Q4:

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

Q5:

Find the shortest distance between the two parallel lines with equations 𝑦 = 2 π‘₯ βˆ’ 7 and 𝑦 = 2 π‘₯ + 3 .

  • A 2 √ 5
  • B 5 √ 2
  • C 2 √ 2
  • D 4 √ 2
  • E √ 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 ( π‘Ž , 2 ) and 𝐡 ( βˆ’ 1 0 , 3 ) , find all possible values of π‘Ž .

  • A π‘Ž = βˆ’ 4 or π‘Ž = βˆ’ 1 6
  • B π‘Ž = 1 6 or π‘Ž = 4
  • C π‘Ž = 2 6 or π‘Ž = βˆ’ 4 6
  • D π‘Ž = 4 6 or π‘Ž = βˆ’ 2 6

Q7:

What is the distance between the parallel lines 2 π‘₯ + 7 𝑦 βˆ’ 2 2 = 0 and 2 π‘₯ + 7 𝑦 + 4 4 = 0 ?

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

Q8:

What is the distance between the parallel lines 3 π‘₯ + 4 𝑦 + 1 1 = 0 and 3 π‘₯ + 4 𝑦 βˆ’ 2 2 = 0 ?

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

Q9:

What is the distance between the parallel lines π‘₯ βˆ’ 3 𝑦 βˆ’ 1 0 = 0 and π‘₯ βˆ’ 3 𝑦 βˆ’ 2 0 = 0 ?

  • A √ 1 0
  • B 2 √ 1 0 5
  • C 5 √ 2
  • D1
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