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

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.

  • A1161717 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|2𝑎×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+𝑠5,7.

  • A8936
  • B897474
  • C197474
  • 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).

  • A11105 units length
  • B1016 units length
  • C8105 units length
  • D825 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
  • B716565 length units
  • C626565 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+8𝑦5=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+𝑘2,4 and 19,17+𝑘7,14?

  • A7133
  • B7155
  • C3755
  • D715

Q9:

What is the distance between the parallel lines 𝑥6𝑦+11=0 and 𝑥6𝑦+22=0?

  • A1155
  • B113737
  • C353737
  • 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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