Lesson Worksheet: Perpendicular Distance from a Point to a Line on the Coordinate Plane Mathematics

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In this worksheet, we will practice finding the perpendicular distance between a point and a straight line or between two parallel lines on the coordinate plane using the formula.

Q1:

Find the length of the perpendicular drawn from the point 𝐴(1,9) to the straight line −5𝑥+12𝑦+13=0.

  • A116√1717 length units
  • B11613 length units
  • C116169 length units
  • D12613 length units

Q2:

Determine the length of the perpendicular from a point 𝐴(0,0) to the line 𝑎𝑥+𝑏𝑦+𝑐=0.

  • A|𝑐|√𝑎+𝑏
  • B2|𝑐|√𝑎+𝑏
  • C|𝑐|√𝑎×2+𝑏×2
  • D|𝑐|2√𝑎×2+𝑏×2
  • E|𝑐|√𝑎+𝑏

Q3:

Find the length of the perpendicular from the point (5,7) to the straight line r=⟨−7,6⟩+𝑠⟨−5,7⟩.

  • A89√36
  • B89√7474
  • C19√7474
  • D8974

Q4:

Find the length of the perpendicular drawn from the point 𝐴(−1,−7) to the straight line passing through the points 𝐵(6,−4) and 𝐶(9,−5).

  • A11√105 units length
  • B√1016 units length
  • C8√105 units length
  • D8√25 units length

Q5:

Find the length of the perpendicular line drawn from the point 𝐴(−8,5) to the straight line that passes through the point 𝐵(2,−4) and whose slope is =−8.

  • A4965 length units
  • B71√6565 length units
  • C62√6565 length units
  • D718 length units

Q6:

Consider the parallelogram whose vertices have coordinates 𝐴(1,1), 𝐵(4,5), 𝐶(5,12), and 𝐷(2,8). Calculate the area of the parallelogram to the nearest square unit.

Q7:

If the length of the perpendicular drawn from the point (−5,𝑦) to the straight line −15𝑥+8𝑦−5=0 is 10 length units, find all the possible values of 𝑦.

  • A𝑦=−433 or 𝑦=253
  • B𝑦=−30 or 𝑦=30
  • C𝑦=−252 or 𝑦=252
  • D𝑦=−30 or 𝑦=252

Q8:

What is the distance between lines ⟨−16,−16⟩+𝑘⟨2,4⟩ and ⟨19,−17⟩+𝑘⟨7,14⟩?

  • A71√33
  • B71√55
  • C37√55
  • D715

Q9:

What is the distance between the parallel lines 𝑥−6𝑦+11=0 and 𝑥−6𝑦+22=0?

  • A11√55
  • B11√3737
  • C35√3737
  • D1137

Q10:

Determine the length of the perpendicular from a point 𝐴(𝑥,𝑦) to the line 𝑦=0.

  • A|𝑦|
  • B|𝑦||𝑥|
  • C|𝑥|
  • D|𝑥|+|𝑦|
  • E0

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