Lesson Worksheet: Perpendiculars and Distance Mathematics

In this worksheet, we will practice finding the perpendicular distance between a point and a straight line and between two parallel lines.

Q1:

Find the length of the perpendicular drawn from the point 𝐴(1,9) to the straight line βˆ’5π‘₯+12𝑦+13=0.

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

Q2:

Find the shortest distance between the line 𝑦=12π‘₯βˆ’2 and the point 𝐴(9,βˆ’10).

  • A√5
  • B5√5
  • C√3
  • D√277
  • E√11

Q3:

Find the shortest distance between the line 𝑦=1 and point 𝐴(1,7).

Q4:

Find the perpendicular distance between the point 𝐴(2,20) and the π‘₯-axis.

Q5:

What is the distance between the point (βˆ’9,βˆ’10) and the line of slope 1 through (3,βˆ’7)?

  • A29√22 length units
  • B23√22 length units
  • C9√22 length units
  • D5√22 length units

Q6:

Find the length of the perpendicular from the point (βˆ’19,βˆ’13) to the 𝑦-axis.

Q7:

Find the length of the perpendicular from the point (βˆ’22,βˆ’5) to the π‘₯-axis.

Q8:

Find the length of the perpendicular drawn from the origin to the straight line βˆ’3π‘₯+4π‘¦βˆ’21=0 rounded to the nearest hundredth.

  • A4.20Β length units
  • B14.85Β length units
  • C0.24Β length units
  • D21.00Β length units

Q9:

Find the length of the perpendicular drawn from the point 𝐴(βˆ’1,βˆ’7) to the straight line passing through the points 𝐡(6,βˆ’4) and 𝐢(9,βˆ’5).

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

Q10:

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

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

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