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Distance on the coordinate plane worksheet

Grade 8 math, Common Core 8.G.B.8. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

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Distance on the coordinate plane

Grade 8 math, Common Core 8.G.B.8

Find the distance between each pair of points. Round to the nearest tenth if needed.

  1. 1.
    (−1, −6) and (−9, 9)
  2. 2.
    (−3, 1) and (3, −4)
  3. 3.
    (−6, 1) and (−1, 0)
  4. 4.
    (3, 0) and (10, −5)
  5. 5.
    (2, −1) and (14, 4)
  6. 6.
    (2, −1) and (7, −5)
  7. 7.
    (−2, 3) and (3, −4)
  8. 8.
    (5, −4) and (9, −7)
  9. 9.
    (−2, −2) and (−6, 1)
  10. 10.
    (−5, 5) and (−29, −2)
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Distance on the coordinate plane

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. 17 units

    Horizontal 8, vertical 15√(8² + 15²) = √289 = 17

  2. 2. √61 ≈ 7.8 units

    Horizontal 6, vertical 5√(6² + 5²) = √61 ≈ 7.8

  3. 3. √26 ≈ 5.1 units

    Horizontal 5, vertical 1√(5² + 1²) = √26 ≈ 5.1

  4. 4. √74 ≈ 8.6 units

    Horizontal 7, vertical 5√(7² + 5²) = √74 ≈ 8.6

  5. 5. 13 units

    Horizontal 12, vertical 5√(12² + 5²) = √169 = 13

  6. 6. √41 ≈ 6.4 units

    Horizontal 5, vertical 4√(5² + 4²) = √41 ≈ 6.4

  7. 7. √74 ≈ 8.6 units

    Horizontal 5, vertical 7√(5² + 7²) = √74 ≈ 8.6

  8. 8. 5 units

    Horizontal 4, vertical 3√(4² + 3²) = √25 = 5

  9. 9. 5 units

    Horizontal 4, vertical 3√(4² + 3²) = √25 = 5

  10. 10. 25 units

    Horizontal 24, vertical 7√(24² + 7²) = √625 = 25

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About distance on the coordinate plane

To find the distance between two points, draw a right triangle with the segment as its hypotenuse. The legs are the horizontal and vertical distances between the points, so the distance is √((x₂ − x₁)² + (y₂ − y₁)²): the Pythagorean theorem on the coordinate plane.

Worked example 1

(0, −5) and (1, −10)
  1. Step 1.Horizontal 1, vertical 5
  2. Step 2.√(1² + 5²) = √26 ≈ 5.1

Answer: √26 ≈ 5.1 units

Worked example 2

(−5, −2) and (3, −8)
  1. Step 1.Horizontal 8, vertical 6
  2. Step 2.√(8² + 6²) = √100 = 10

Answer: 10 units

Worked example 3

(3, 4) and (−9, 9)
  1. Step 1.Horizontal 12, vertical 5
  2. Step 2.√(12² + 5²) = √169 = 13

Answer: 13 units

Watch out for

  • Find the horizontal and vertical distances first.
  • Squaring makes negatives positive, so the order of subtraction doesn’t matter.
  • If the points share an x or y value, just subtract the other coordinates.

Practice distance on the coordinate plane online

On StudyWiz, your kid can practice distance on the coordinate plane with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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