Grade 6 Math · Topic 30

Reflecting Points Across the Axes

Reflecting a point across an axis flips its position to the mirror-image side. Two simple rules cover most cases: reflecting across the x-axis flips the sign of y, and reflecting across the y-axis flips the sign of x.

Lesson alignment: 6.NS.C.6.b · Take your time. You can return to this lesson whenever you need it.

Explore visually

Reflect a point across an axis

Choose an axis and see which coordinate changes sign while the other stays the same.

Think first: When a point reflects across this axis, which coordinate do you expect to change sign?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Reflect (3, -5) across the x-axis.

Reflecting across the x-axis keeps x the same and flips the sign of y: (3, -5) → (3, 5).

Answer: (3, 5)

Worked example 2

Reflect (-2, 6) across the y-axis.

Reflecting across the y-axis keeps y the same and flips the sign of x: (-2, 6) → (2, 6).

Answer: (2, 6)

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. (4, 3) across x-axis →
    Check

    (4,-3)

  2. (-5, 2) across x-axis →
    Check

    (-5,-2)

  3. (7, -1) across y-axis →
    Check

    (-7,-1)

  4. (-6, -8) across y-axis →
    Check

    (6,-8)

  5. (2, 9) across x-axis →
    Check

    (2,-9)

  6. (-3, 0) across y-axis →
    Check

    (3,0)

  7. (5, -4) across x-axis →
    Check

    (5,4)

  8. (-1, 7) across x-axis →
    Check

    (-1,-7)

Try this situation 1

A boat is at (6, 4). Its mirror image across a north--south wall (the y-axis) shows it at what coordinates?

Show a worked solution

Answer: (-6, 4).

Reflecting across the y-axis flips x: (6,4) → (-6,4).

Try this situation 2

Point P is at (-3, -7). Find P's reflection across the x-axis.

Show a worked solution

Answer: (-3, 7).

Reflecting across the x-axis flips y: (-3,-7) → (-3,7).

Fresh questions · saved on this device

Practice this skill

12 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. Which point is the reflection of (4, 5) across the y-axis?

2. A point starts at (-5, 3). It is reflected across the y-axis, then reflected across the x-axis. What are its final coordinates?

3. Point T(0, 2) is reflected across the y-axis. What are the coordinates of the image T'?

4. Point P is located at (3, -2). If Point P is reflected across the x-axis, what are the coordinates of the new point?

5. Point (2, 6) is reflected first across the x-axis, then across the y-axis. What are the final coordinates?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Integers & the Coordinate Plane quiz ↗Try a full practice test ↗