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The coordinate plane worksheet

Grade 6 math, Common Core 6.NS.C.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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The coordinate plane

Grade 6 math, Common Core 6.NS.C.8

Answer each question about points on the coordinate plane.

  1. 1.
    How far apart are (2, 4) and (2, 6)?
  2. 2.
    How far apart are (−4, −8) and (−4, −5)?
  3. 3.
    In which quadrant is the point (6, 7)?
  4. 4.
    Reflect (−4, −9) across the x-axis. What are the new coordinates?
  5. 5.
    How far apart are (8, 3) and (8, −7)?
  6. 6.
    Reflect (−6, −2) across the x-axis. What are the new coordinates?
  7. 7.
    How far apart are (−2, −3) and (−2, 8)?
  8. 8.
    Reflect (−9, −5) across the y-axis. What are the new coordinates?
  9. 9.
    How far apart are (7, 2) and (7, −1)?
  10. 10.
    How far apart are (−3, 4) and (−3, 5)?
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: The coordinate plane

Grade 6 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. 2 units

    Same x, so subtract the y-values: |4 − 6| = 2

  2. 2. 3 units

    Same x, so subtract the y-values: |−8 − (−5)| = 3

  3. 3. Quadrant I

  4. 4. (−4, 9)

    Change the sign of the y-coordinate

  5. 5. 10 units

    Same x, so subtract the y-values: |3 − (−7)| = 10

  6. 6. (−6, 2)

    Change the sign of the y-coordinate

  7. 7. 11 units

    Same x, so subtract the y-values: |−3 − 8| = 11

  8. 8. (9, −5)

    Change the sign of the x-coordinate

  9. 9. 3 units

    Same x, so subtract the y-values: |2 − (−1)| = 3

  10. 10. 1 units

    Same x, so subtract the y-values: |4 − 5| = 1

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

About the coordinate plane

A point on the coordinate plane is written (x, y): first how far right or left, then how far up or down. The axes split the plane into four quadrants, numbered I to IV counterclockwise from the top right. Reflecting a point across an axis changes the sign of one coordinate.

Worked example 1

Reflect (9, 9) across the x-axis. What are the new coordinates?
  1. Step 1.Change the sign of the y-coordinate

Answer: (9, −9)

Worked example 2

How far apart are (−3, 8) and (−8, 8)?
  1. Step 1.Same y, so subtract the x-values: |−3 − (−8)| = 5

Answer: 5 units

Worked example 3

Reflect (−5, 3) across the x-axis. What are the new coordinates?
  1. Step 1.Change the sign of the y-coordinate

Answer: (−5, −3)

Watch out for

  • x comes first, like walking to the elevator (left or right) before riding it (up or down).
  • Reflect across the x-axis: change the sign of y. Reflect across the y-axis: change the sign of x.
  • For two points on the same vertical line, the distance is the difference of the y-values. If one is negative, add the distances from 0.

Practice the coordinate plane online

On StudyWiz, your kid can practice 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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