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Worksheet: Error Estimation for a Series

Q1:

Consider the following two parallel lines:

  • Line A: 𝑦 = 2 π‘₯ + 3 ,
  • Line B: 𝑦 = 2 π‘₯ βˆ’ 7 .

What is the slope of any line that is perpendicular to lines A and B?

  • A2
  • B βˆ’ 2
  • C 1 2
  • D βˆ’ 1 2
  • E βˆ’ 1

The point ( 0 , 3 ) is on line A. Find the coordinates of the point on line B that is closest to ( 0 , 3 ) .

  • A ( 4 , 1 )
  • B ( 2 , βˆ’ 3 )
  • C ( 1 , βˆ’ 5 )
  • D ( 0 , βˆ’ 7 )
  • E ( 3 , βˆ’ 1 )

Hence, find the shortest distance between lines A and B. Give an exact answer.

  • A √ 1 7
  • B4
  • C √ 2 0
  • D5
  • E6

Q2:

Find the shortest distance between the following two parallel lines: If necessary, round your answer to 2 decimal places.