Lesson Worksheet: The Distance between Two Points Mathematics

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In this worksheet, we will practice finding the distance between two points on the coordinate plane using the Pythagorean theorem.

Q1:

The distance between (𝑎,5) and (1,1) is 5. What are the possible values of 𝑎?

  • A𝑎=2 or −4
  • B𝑎=−2 or 4
  • C𝑎=2 or 4
  • D𝑎=−2 or −4

Q2:

Which of the following points is at a distance of 5√2 from the origin?

  • A5√2,5√2
  • B(5,5)
  • C(0,5)
  • D(5,0)

Q3:

Find the distance between the point (−2,4) and the point of origin.

  • A2√2 length units
  • B3√2 length units
  • C2√5 length units
  • D√6 length units

Q4:

Find the distance between 𝐿(−2,−8) and 𝑀(−6,−9), giving your answer in radical form if necessary.

  • A15
  • B√15
  • C√5
  • D17
  • E√17

Q5:

Find the distance between the points 𝐴 and 𝐵.

  • A4 length units
  • B16 length units
  • C√58 length units
  • D2√13 length units
  • E√10 length units

Q6:

Two baseball posts were positioned at (9,3) and (6,9). Find the distance between the posts giving the answer to one decimal place.

Q7:

Khalid is making a map of his local area measured in meters. The coffee shop is at (−5,−4) and the Italian restaurant is at (0,6). Find the distance between the coffee shop and the Italian restaurant giving the answer to one decimal place.

Q8:

What is the distance between the point 𝐴 and the origin?

  • A2√5 length units
  • B√6 length units
  • C3√2 length units
  • D2√2 length units

Q9:

Find the distance between the points (4,5) and (6,−2).

  • A√51 length units
  • B√53 length units
  • C13 length units
  • D√11 length units
  • E3 length units

Q10:

Find the distance between the two points in the figure below, giving your answer in radical form if necessary.

  • A√35
  • B5√5
  • C√37
  • D7
  • E5√3

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